100 Points! Expand (2d+3)^6. Please show as much work as possible. Thank you! Photo attached.

Answer: y^3/5

Step-by-step explanation:

Answer:

We can factor out a y^3 term from the expression y^3 - y^5:

y^3 - y^5 = y^3(1 - y^2)

So, y^3 - y^5 can be written as the product y^3(1 - y^2).

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 exponential function showing the relationship is y = 2300(1 + 0.12)^t

The exponential function showing the relationship between y and t can be written as:

y = 2300(1 + 0.12)^t

where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.

This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.

In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.

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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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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 sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.

In the given question,

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.

Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.

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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~~~

Answer:

6.5875 × 10^2

Step-by-step explanation:

Standard form format is: a×10^b

A number is written in standard form when it is represented as a decimal number times a power of 10.

As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 10^8.

Example: Convert 459,608 to Standard Form

Move the decimal 5 places to the left to get 4.59608

a = 4.59608

We moved the decimal to the left so b is positive

b = 5

The number 459,608 converted to standard form is 4.59608 x 10^5

hope this helps <3

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 agency made $28,275 in commission on the house.

The agent earned $5,655 in commission on the sale of the house.

We first need to calculate the amount of commission that the agency received.

The commission rate for the agency is 7.5%, so we can find the commission amount by multiplying the sale price of the house by 7.5% in decimal form:

Commission for the agency = $377,000 x 0.075 = $28,275

Therefore, the agency made $28,275 in commission on the house.

To calculate how much the agent earned in commission, we need to find 20% of the commission amount that the agency received:

Commission for the agent = $28,275 x 0.20 = $5,655

Therefore, the agent earned $5,655 in commission on the sale of the house.

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With regard to the linear functions,

Part 1:

To find the point where the cost equals the revenue, we need to set the two equations equal to each other and solve for x:

Revenue: y=1.2x

Cost: y = 0.4x+32

1.2x = 0.4x + 32 (substitute y with 1.2x for revenue and y with 0.4x+32 for cost)

0.8x = 32 (subtract 0.4x from both sides)

x = 40 (divide both sides by 0.8)

Now that we have found x=40, we can find y by plugging it into either equation. Let's use the revenue equation:

y = 1.2x

y = 1.2(40)

y = 48

Therefore, the point where the cost equals the revenue is (40, 48).

Part 2:

The point (40, 48) represents the number of batteries that need to be produced in order for the cost to equal the revenue. In other words, if the company produces 40 thousand batteries, they will earn 48 thousand dollars in revenue and spend 32 thousand dollars in costs, resulting in a profit of 16 thousand dollars.

Part 3:

To check if our results from Part 1 correspond with the graph, we can plot the two equations on the same graph and look for the point of intersection.

As we can see from the graph, the two lines intersect at the point (40, 48), which confirms our result from Part 1.

Part 4:

Profit is found by subtracting cost from revenue, so the profit equation would be:

Profit: y = 1.2x - (0.4x + 32)

Simplifying the equation:

y = 1.2x - 0.4x - 32

y = 0.8x - 32

Part 5:

To find the profit from producing 100 thousand batteries, we can plug x=100 into the profit equation we found in Part 4:

y = 0.8x - 32

y = 0.8(100) - 32

y = 48

Therefore, the profit from producing 100 thousand batteries would be 48 thousand dollars.

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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: 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:

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:125 meters

Step-by-step explanation:

volume of a cube is w^3

w=5

5*5*5

125 meters

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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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.

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:

The exact value of the expressions 6os(a + 6), 6in(a + b) and tan(a + beta) under the given conditions is 6*cos(A/6), -6*sin(b) and tan(a) + 12/13 respectively.

Expression is a way for an individual to convey their thoughts, feelings, beliefs, and ideas. It can be done through different forms such as verbal communication, art, dance, music, writing, and body language. Expression allows people to express themselves in a way that can be understood by others. It can help to create a connection between people by allowing them to connect with one another on a deeper level.

6os(a + 6) = 6*sin(a + 6) = 6*sin(a)cos(6) + 6*cos(a)sin(6)
Since a lies in quadrant 1, sin(a) = 1 and cos(a) = 0. Therefore,
6os(a + 6) = 6*sin(a)cos(6) + 6*cos(a)sin(6) = 6*1*cos(6) + 6*0*sin(6) = 6*cos(6) = 6*cos(A/6)
6in(a + b) = 6*cos(a + b) = 6*cos(a)cos(b) - 6*sin(a)sin(b)
Since a lies in quadrant 1, sin(a) = 1 and cos(a) = 0. Therefore,
6in(a + b) = 6*cos(a)cos(b) - 6*sin(a)sin(b) = 6*0*cos(b) - 6*1*sin(b) = -6*sin(b)
tan(a + beta) = tan(a) + tan(beta)
Since sin(0) = 12/13, tan(beta) = 12/13. Therefore,
tan(a + beta) = tan(a) + tan(beta) = tan(a) + 12/13
The exact value of the expressions 6os(a + 6), 6in(a + b) and tan(a + beta) under the given conditions is 6*cos(A/6), -6*sin(b) and tan(a) + 12/13 respectively.

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Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.

Plugging in the radius r = 12 meters, we get:

Surface area = 2π(12)^2

Surface area = 2π(144)

Surface area ≈ 904.78

Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.

So the answer is: 967 meters squared.

Step-by-step explanation:

The degree measure of the angles are;

1. 5π/3 = 300°

2 3π/4 = 135°

3. 5π/6 = 150°

4. -3π/2 = 90°

A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.

A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.

therefore π = 180°

1. 5π/ 3 = 5×180/3 = 300°

2. 3π/4 = 3× 180/4 = 540/4 = 135°

3. 5π/6 = 5×180/6 = 150°

4. - 3π/2 = -3 × 180/2 = -270° = 90°

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Answer:

40 m²

Step-by-step explanation:

Area of triangle:

To find the area of triangle, multiply the base and area and then divide it by 2.

      base = b = 8 m

height      = h = 10m

      [tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]

                                     [tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]

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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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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Answer:

y = 0.028t + 230,000 Step-by-step explanation: We know t = number of years since the start of the study y = be the city's population Each year the population

Step-by-step explanation:

Answer:

[tex]\frac{64}{25}[/tex]

Step-by-step explanation:

[tex]\frac{4^{3} }{5^{2} }[/tex]

4³ = 64

5² = 25

[tex]\frac{64}{25}[/tex] is already in simplest form, so it is the answer.

since 3/5 y is 6 to find what 1/5 y is we divide 6 by 3 which is 2 so 1/5 y=2. Now to find the value of y we multiply that by 5 and since 2*5=10 y=10. Also pls mark as brainliest answer

40% of Canadians read at least 10 books a year.

A percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.

If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:

2/5

We can multiply this fraction by 100 to turn it to a percentage:

(2/5) x 100 = 40%

Therefore, 40% of Canadians read at least 10 books a year.

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