factorize the following using difference between squares

2k³ - 3k²-2k+3

The probability that the card that Olga turns over has a rose on it would be 4/5.

Since, Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that;

There are 5 cards with a picture of a rose and 1 card with a picture of a daisy.

Olga keeps all the cards face down on the table with the pictures hidden and mixes them up.

Then , Total number of cars after Olga removed one rose card from the table is,

4 rose cards + 1 Daisy card

= 5

Therefore, the probability divide the number of rose cards left by the total number of cards left is,

= 4/5

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Answer: D

Step-by-step explanation:

The left side of a stem-leaf plot is the first part of the number and the right sides are the leaves.  so list of numbers for city 1 is:

8, 11, 15, 17, 18, 23, 32, 35, 40, 54, 58, 59

median is the middle number and range is if you subracted the first and last numbers.

A. is out The medians are not the same

B. is out The median for City 2 is greater

C. is out. The ranges are not the same

D. is correct.  Range for city 1 is: 59-8=51  Range for city 2 is: 61-31=30

Nuclear fusion involves the combination of two light nuclei to form a heavier nucleus with emission of energy.

Since,

A nuclear reaction equation is a representation of the change that takes place as one nucleus is converted to another. A nuclear transformation could be any of the following;

⇒ Nuclear fission

⇒ Nuclear fusion

⇒ Transmutation

We can know that a nuclear fusion is taking place when two nuclei come together to form a larger nucleus and emit energy. I would identify a nuclear fusion when;

⇒ Two light atom combine to give a larger nucleus

⇒ Tremendous energy is produced

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Answer:

10. a. no

b. yes

c. no

d. no

e. no

11. a. yes

b. no

c. yes

d. no

e. no

Since the diameter of this circle is 7 cm, its area to the nearest whole number include the following: 39 square centimeters.

In Mathematics and Geometry, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 7/2 = 3.5 centimeters.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = 3.142 × 3.5²

Area of circle = 38.5 ≈ 39 square centimeters.

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Answer:

Step-by-step explanation:

48 over 12 = 4 is the answer

The percentage of the class that are 13 years old can be found to be 43.75%

We have,

Number of 13 year olds = 21

Number of 15 year olds = 27

So, Total students

= Number of 13 year olds + Number of 15 year olds

= 21 + 27

= 48 students

and, the percentage of students who are aged 13 is

= 21 / 48 x 100 %

= 0. 4375 x 100 %

= 43. 75 %

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In case of three friends decide to go out to eat, and then go shopping there are 20 possibilities are there for their big night out.

The problem is asking for the total number of possibilities when three friends decide to go out to eat and then go shopping. Since they can only pick one restaurant and one store, we can use the multiplication principle to determine the total number of possibilities.

There are 5 options for the restaurant and 4 options for the store, so the total number of possibilities is 5 x 4 = 20. Therefore, there are 20 different combinations of restaurant and store that the three friends can choose from for their big night out.

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Therefore, the population is at a maximum approximately 25 hours after the culture was started.

A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.

Here,

To find the time at which the population is at a maximum, we need to find the time when the rate of change of population, or the derivative of p(t), is zero.

p(t) = -1715t² + 85,000t + 10,000

p'(t) = -3430t + 85,000

Setting p'(t) = 0, we get:

-3430t + 85,000 = 0

Solving for t, we get:

t = 24.85

Rounding to the nearest hour, we get:

t ≈ 25

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Answer:

To solve for n, we can multiply both sides of the equation by 10:

n/10 = 0.41

n = 10 x 0.41

n = 4.1

Therefore, n is approximately 4.1.

Step-by-step explanation:

The mean of this data set is ³/₅ inches as a fraction in simple form.

The mean refers to the average of the data set.

The average can be determined as the quotient of the total data value divided by the number of items in the data set.

The length of the first piece of ribbon = ¹/₄ inches

The length of the second piece of ribbon = 1¹/₃ inches

The length of the third piece of ribbon = ²/₃ inches

The length of the fourth piece of ribbon = ¹/₄ inches

The length of the fifth piece of ribbon = ¹/₂ inches

The total length of the five pieces of ribbon = 3 inches

The mean = ³/₅ inches (3 ÷ 5)

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The trigonometric relation is solved and the unit circle is plotted

Given data ,

Let the unit circle be represented as A and B

Now , in figure A , we get

The radius of the circle is r = 5 units

And the point on the circle is P ( 5 , 5 )

So , the height of unit circle is h = 5 units

Now , the hypotenuse of the circle is = 2√5 units

From the trigonometric relation , we get

sin θ = opposite / hypotenuse

sin z = √5 / 2√5

sin z = 1/2

Taking inverse on both sides , we get

z = 30°

So , the measure of rotation is 60° counterclockwise

In figure B , we get

The radius of the circle is r = 5 units

And the point on the circle is P ( 5 , -5 )

So , the height of unit circle is h = -5 units

Now , the hypotenuse of the circle is = 2√5 units

From the trigonometric relation , we get

sin θ = opposite / hypotenuse

sin z = √5 / 2√5

sin z = -1/2

Taking inverse on both sides , we get

z = -30°

So , the measure of rotation is 30° clockwise

Hence , the trigonometric relation is solved

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Answer:

The car came to a complete stop during segment C to D, because the distance did not change over time.

The car traveled back toward its starting position during segment D to E, because the distance decreased over time.

The car traveled the fastest during segment B to C, because the slope of the graph was the steepest.

The car traveled at an average speed of 12 km/hr during segment A to B, because the slope of the graph was 12 km/hr.

Step-by-step explanation:

As per the mention equation, the solutions in the interval [0, 2π) are calculated out to be x = π/4, 3π/4, 5π/4, 7π/4

We know that:

2 sin²(x) = 1

sin²(x) = 1/2

Taking the square root of both sides, we get:

sin(x) = ±√(1/2)

So, either:

sin(x) = √(1/2) = 1/√2

or

sin(x) = -√(1/2) = -1/√2

To find the solutions in the interval [0, 2π), we need to look for the values of x that satisfy each of these equations.

For the first equation, sin(x) = 1/√2, we know that this is true for x = π/4 or x = 7π/4, since sin(π/4) = sin(7π/4) = 1/√2.

For the second equation, sin(x) = -1/√2, we know that this is true for x = 3π/4 or x = 5π/4, since sin(3π/4) = sin(5π/4) = -1/√2.

Therefore, the solutions in the interval [0, 2π) are:

x = π/4, 3π/4, 5π/4, 7π/4

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If the tax had been levied on producers instead of consumers, the effect on the quantity sold would have been smaller is True. The amount of tax on a case of cider is $4. Of this amount, the burden that falls on consumers is $3 per case, and the burden that falls on producers is $1 per case.

This is because producers would have had to bear the full burden of the tax, reducing their incentive to produce and sell cider. To calculate the tax burden on consumers, we can subtract the price per case before the tax ($11) from the price after the tax ($15), which equals $4. Then, we subtract the amount of the tax that falls on producers ($1) to get the amount of the tax burden on consumers ($3).

To calculate the tax burden on producers, we can subtract the amount they receive per case after the tax ($9) from the price per case before the tax ($11), which equals $2. This $2 is split between the producers and the government, with the producers bearing $1 of the burden.

This could result in a decrease in the supply of cider, leading to higher prices and less demand from consumers. By taxing consumers instead, the government can still collect revenue from the tax while minimizing the impact on the supply and demand of cider in the market.

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Answer:  so, if l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the centre, then; θ = l/r, where θ is in radians

Central angle, θ = (Arc length × 360º)/(2πr) degrees or Central angle, θ = Arc length/r radians, where r is the radius of the circle. The formula is Degrees = Radians × 180 / π and it can be used for both positive and negative values. The sector of a circle is a slice of a circle, bound by two radiuses and an arc of the circumference. We identify sectors of a circle using their central angle. The central angle is the angle between the two radiuses. Sectors with a central angle equal to 90° are called quadrants.

Alex's house is due west of Lexington and due south of Norwood. using Pythagorean theorem, the Norwood is 10 miles from Alex's house, measured in a straight line.

The Pythagorean theorem is a fundamental concept in mathematics that relates to the sides of a right triangle.

It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to solve this problem.

Let x represents the distance we want to find.

Using the Pythagorean theorem, we can write:

[tex]x^2 = 6^2 + 8^2\\x^2 = 36 + 64\\x^2 = 100[/tex]

x = sqrt(100)

x = 10

Therefore, Norwood is 10 miles from Alex's house, measured in a straight line.

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Answer:

90

Step-by-step explanation:

To find how many 18-inch pieces of ribbon there are in 1620 inches, simply divide 1620 by 18.

1620/18 = 90

For the original question, we know that each roll of ribbon is 9 feet long. To convert to inches, multiply 9 by 12.

9*12 = 108

Now, to find how many 18-inch pieces of ribbon there are in 108 inches,  divide 108 by 18.

108/18 = 6

Since we have 15 rolls of ribbon, multiply 6 by 15.

6*15 = 90

∴ The dressmaker can cut ninety 18-inch pieces from 15 rolls or ribbon.

Answer:

The half-life of carbon-14 is 5,730 years. This means that every 5,730 years, half of the carbon-14 in a sample will decay. So, if a sample contains 32% of its original amount of carbon-14, it is about 2 * 5,730 = 11,460 years old.

However, it is essential to note that radiocarbon dating is not an exact science. There is a margin of error of about 20 years. So, the skull's actual age could be between 11,260 and 11,660 years old.

Here is a formula that can be used to calculate the age of a sample using radiocarbon dating:

```

Age = (5,730 * ln(A/Ao)) / ln(2)

```

Where:

* Age is the age of the sample in years

* A is the amount of carbon-14 in the sample

* Ao is the original amount of carbon-14 in the sample

* ln is the natural logarithm function

In this case, A = 0.32 and Ao = 1.0. So, the age of the skull is:

```

Age = (5,730 * ln(0.32) / ln(2)) = 11,460 years

```

Step-by-step explanation:

Answer:

4535 years.

Step-by-step explanation:

The formula used to calculate the age of a sample by carbon-14 dating is3:

t=−0.693ln(N0​Nf​​)​×t1/2​

where:

t is the age of the sample

Nf is the number of carbon-14 atoms in the sample after time t

N0 is the number of carbon-14 atoms in the original sample

t1/2 is the half-life of carbon-14 (5730 years)

In your case, the skull contains 32% of its original amount of carbon-14, which means that Nf/N0 = 0.32. You can plug in this value and the half-life into the formula and get:

t=−0.693ln(10.32​)​×5730

Using a calculator, you can simplify this expression and get:

t=−1.139×−0.693×5730

t=4534.7

Answer:

1. 2-way frequency table goes with the 1st one  

2. Marginal frequency goes with the 4th one  

3. joint frequency goes with the 3rd one

4. conditional frequency goes with the 2nd one

The height of the cylinder will be 18 inches.

Given that:

Volume, V = 2,769.48 cubic inches

Radius, r = 7 inches

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be given as,

V = π r²h cubic units

The height of the cylinder is calculated as,

2,769.48 = 3.14 x 7² x h

2,769.48 = 153.86h

h = 18 inches

The height of the cylinder will be 18 inches.

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The constant of variation for the case is 2 centimeters per night.

A graph is a non-linear kind of data structure made up of nodes or vertices and edges. The edges connect any two nodes in the graph, and the nodes are also known as vertices. This graph has a set of vertices V= { 1,2,3,4,5} and a set of edges E= { (1,2),(1,3),(2,3),(2,4),(2,5),(3,5),(4,50 }.

The graph shown in the problem has length as the vertical axis and nights as the horizontal axis.

The points through which the straight line passes are (0, 0) and (10, 20).

The equation of the line can be written as follows,

=> [tex]\frac{y-0}{x-0}=\frac{20-0}{10-0}[/tex]

=> [tex]\frac{y}{x}=\frac{20}{10}[/tex]

=> y = 2x

Thus, the above equation implies that y and x are proportional and 2 is constant of variation.

Hence, the constant of variation for the given case is 2 centimeters per night.

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The given question is incomplete, So i take the similar question:

This graph shows how the total length Kimi has knit depends on the number of nights she has spent knitting.

​What is the constant of variation?

____ centimeters per night

Answer:

The glass cannot fit through the door.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let the height of the door be h.

We know that the diagonal of the glass must be able to fit through the door, so we can set up the following equation:

sqrt(8^2 + h^2) <= 3

Squaring both sides of the inequality, we get:

64 + h^2 <= 9

Subtracting 64 from both sides, we get:

h^2 <= -55

Since a square of a real number cannot be negative, there is no solution to this inequality.

Therefore, the glass cannot fit through the door, regardless of the height of the door.

The door must be at least √55 feet tall, which is approximately 7.42 feet, for the 8-foot wide glass to pass through the 3-foot wide door.

To determine how tall the door must be for the glass to pass through, we first need to calculate the height of the glass. Unfortunately, the height of the glass is not provided in the question. Assuming that the height of the glass is less than or equal to the height of the door, we can proceed as follows:

Let's say the height of the glass is h feet. Then, we know that the glass is a rectangular shape with dimensions of 8 feet by h feet. To pass through the door, the glass needs to be able to fit horizontally and vertically through the opening.

Since the door is 3 feet wide, the glass needs to be able to fit through the opening when turned on its side. Therefore, the height of the glass cannot exceed 3 feet.

So, the door must be at least 3 feet tall for the glass to pass through. However, this assumes that the height of the glass is less than or equal to 3 feet. If the height of the glass is greater than 3 feet, then the door would need to be taller to accommodate the glass.

To determine the minimum height the door must be for the 8-foot wide glass to pass through the 3-foot wide door, you can use the Pythagorean theorem. The glass will need to be tilted diagonally as it passes through the door. Let's label the door's height as 'h' and use the formula:

3² + h² = 8²

9 + h² = 64

h² = 64 - 9
h² = 55
h = √55

The door must be at least √55 feet tall, which is approximately 7.42 feet, for the 8-foot wide glass to pass through the 3-foot wide door.

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Answer:

Its the second one

Step-by-step explanation:

its the second one. i looked it up.

Answer:

Step-by-step explanation:

it is the first one because linear is that is related to a line or in order the input is fine going by one’s but the output is not so the output has a problem and it’s not linear so it’s the first option.

The area of isoceles triangle is  120 square meters

Let us assume that a and c represents the equal sides of isosceles triangle and b represents the base of isosceles triangle such that a = 17 m, b = 16 m and c = 17 m

Let us assume that h represents the height of isosceles triangle.

We know that the formula for the height of isosceles triangle.

h = [tex]\sqrt{a^2-\frac{b^2}{4} }[/tex]

h = [tex]\sqrt{17^2-\frac{16^2}{4} }[/tex]

h = √(225)

h = 15 m

Using the formula for the area of isosceles triangle,

A = 1/2 × base × height

A =  1/2 × b × h

A =  1/2 × 16 × 15

A = 120 sq. m.

Therefore, the required area is  120 sq. m.

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The complete question is:

The sides of isosceles triangle triangle are: 17 m, 17 m and 16 m

Find the area of the isoceles triangle. The area is square meters.

La fuerza con la que es lanzada una pelota de béisbol puede calcularse utilizando la segunda ley de Newton, que establece que la fuerza (F) es igual a la masa (m) multiplicada por la aceleración (a). En este caso, la masa de la pelota es de 0.126 kilogramos y la aceleración es de 3 m/s.

Aplicando la fórmula, la fuerza (F) se calcula de la siguiente manera:

F = m * a

F = 0.126 kg * 3 m/s

F = 0.378 N

Por lo tanto, la fuerza con la que se lanza la pelota de béisbol es de aproximadamente 0.378 Newtons.

Es importante tener en cuenta que este cálculo asume que la aceleración proporcionada es constante y que no hay otras fuerzas que actúen sobre la pelota durante el lanzamiento, como la resistencia del aire. Estas consideraciones pueden afectar la fuerza real experimentada por la pelota en un escenario práctico.

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