Evaluate a−b if a=−2.5 and b=25 . Write your answer in simplest form.

The answer is \(2x\leq 25\) .

It is given that twice of x is at most .

“At most” refers to a maximum amount.

“At most” means that any number less than the number presented is acceptable or true,

In mathematically , it is represented as

\(2x\leq 25\)

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The number of each type of problem that will be assigned to each student is 12

The given parameters are

108 GCF problems

60 LCM problems

180 prime factorization problems

Rewrite as

GCF = 108

LCM = 60

Prime = 180

Express the above numbers as a product of their factors

So, we have

GCF = 2 x 2 x 3 x 3 x 3

LCM = 2 x 2 x 3 x 5

Prime = 2 x 2 x 3 x 3 x 5

Multiply the common factors

So, we have

Common factors = 2 x 2 x 3

Evaluate the products

So, we have

Common factors = 12

Hence, 12 of each type of problem will be assigned to each student

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Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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Answer:

3/10

Hope it helps

Answer:

They're not promise

Step-by-step explanation:

I did it on the calculator

I hope this helps youuu

Have a good day <3

The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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Let A and B be two independent events. If P(B) = 0.5. We can say about P(B|A) that D. It is equal to 0.5.

Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Since A and B are independent events, the probability of event B occurring given that A has occurred (P(B|A)) is the same as the probability of event B occurring without knowledge of whether or not A has occurred (P(B)). Therefore, P(B|A) = P(B) = 0.5.

Hence Option D is correct.

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The total area of the shaded region bounded by the given curves is approximately 4.33 square units.

The given curves are x = 6y² - 6y³ and x = 4y² - 4y. The shaded area is formed between these two curves.

Let’s solve the equation 6y² - 6y³ = 4y² - 4y for y.

6y² - 6y³ = 4y² - 4y

2y² - 2y³ = y² - y

y² + 2y³ = y² - y

y² - y³ = -y² - y

Solving for y, we have:

y² + y³ = y(y² + y) = -y(y + 1)²

y = -1 or y = 0. Therefore, the bounds of integration are from y = 0 to y = -1.

The area between two curves can be calculated as follows:`A = ∫[a, b] (f(x) - g(x)) dx`where a and b are the limits of x at the intersection of the two curves, f(x) is the upper function and g(x) is the lower function.

In this case, the lower function is x = 6y² - 6y³, and the upper function is x = 4y² - 4y.

Substituting x = 6y² - 6y³ and x = 4y² - 4y into the area formula, we get:`

A = ∫[0, -1] [(4y² - 4y) - (6y² - 6y³)] dy

`Evaluating the integral gives:`A = ∫[0, -1] [6y³ - 2y² + 4y] dy`=`[3y^4 - (2/3)y³ + 2y²]` evaluated from y = 0 to y = -1`= (3 - (2/3) + 2) - (0 - 0 + 0)`= 4.33 units² or 4.33 square units (rounded to two decimal places).

Therefore, the total area of the shaded region bounded by the given curves is approximately 4.33 square units.

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Answer:

x=-1/10

Step-by-step explanation:

the question is which equation can be used to find the number of game tickets(g) that Luke bought that night

Step-by-step explanation:

from the total( $10 ) he has used $2 for a hot dog that's 10-2.

this makes the equation g+2= 10

so as we can see the only option that fits would be c

c. 0.25g+2=10

to solve the equation the answer would be 32 game tickets were bought.

If 10 donuts are sold. Then the expected value of the number of sprinkles will be 5.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be given as

E(X) = np

At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data.

If 10 donuts are sold.

Then the number of the sprinkles will be

The probability will be

p = 3/6

p = 0.5

n = 10

Then the expected value of the number of the sprinkles will be

E(x) = 10 x 0.5

E(x) = 5

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The line integral of a vector around the perimeter of a rectangle with corners (x0, y0), (x1, y1), (x2, y2), and (x3, y3) traversed in that order.

What is perimeter?

A closed path which encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose a yard as well as garden is called the perimeter. How far a wheel or circle will roll inside one revolution is determined by its circumference, or perimeter.

To find the perimeter by adding up the side lengths of various shapes.

The line integral starts from the first corner to the last corner of the rectangle and it shows that both the x and y values.

(x0,y0)-first corner point
(x1,y1)-second corner point
(x2,y2)-third corner point
(x3,y3)-four corner point

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As the figure is made for 6 squares, the total area of the figure divided into 6 is the area of one square:

The area of one square is 15 square feet.

The area of a square is equal to the square lenght

Then, as the given squares have area of 15 square feet the measure of the lenght of one square is:

Then, as each side of each square is square root of 15 feet you have the next:

The perimeter of the figure is the sum of all the sides: The figure has 12 sides: 2 sides have a measure of 2square root of 15 feet and the other 10 sides have a measure of square root of 15 feet:

The graph of the absolute value equation y = 2 | x - 2 | + 3 is attached

A graph is pictorial representation of dat the dat is represented in Cartesian coordinate as follows

The given equation is y = 2 | x - 2 | + 3

The input values (x values) are chosen from -2, 0, 2. substituting the x values into the equation gives the y values as follow

for  x = - 2

y = 2 |-2 - 2 | + 3

= 2 | -4| + 3

=-8 + 3      OR      8 + 3

= 5             OR     11

for  x = 0

y = 2 |0 - 2 | + 3

= 2 | -2| + 3

=- 4 + 3      OR      4 + 3

= -1             OR     7

for  x = 2

y = 2 |2 - 2 | + 3

= 2 | 0 | + 3

=-  3    

absolute values yield double output values hence the graph is two straight lines

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer: 2

Step-by-step explanation:

Answer:

need the graph to know

Step-by-step explanation:

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The weight of the dog after 10 days is 5.9 kg.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Weight of the baby on day one = 5 kg

This can be written as,

1 day = 5 kg

The dog grows 0.1 kg each day.

This means,

On the 2nd day, we get,

2 days = 5 + 0.1

2 days = 5.1 kg

The expression for the weight of the dog on n days can be written as,

n days = 5 + (n -1) x 0.1 _____(1)

Now,

After 10 days we get,

n = 10

From (1) we get,

10 days = 5 + (10 - 1) x 0.1

10 days = 5 + 9 x 0.1

10 days = 5 + 0.9

10 days = 5.9 kg

Thus,

The weight of the dog after 10 days is 5.9 kg.

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Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The only number that will equal 64 if it is the power of 2

Answer:

The 8th term of the AP= 113/5 or 22.6

Answer:

22.6

Step-by-step explanation:

Given:

Find the value of a₆:

\(\implies a+a_6=20\)

\(\implies a_6=20-a\)

\(\implies a_6=20-3\)

\(\implies a_6=17\)

Therefore:

General form of an arithmetic sequence:

\(\boxed{a_n=a+(n-1)d}\)

Where:

Substitute a = 3 and a₆ = 17 into the formula and solve for d:

\(\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}\)

Therefore, the equation for the nth term is:

\(\implies a_n=3+(n-1)2.8\)

\(\implies a_n=3+2.8n-2.8\)

\(\implies a_n=2.8n+0.2\)

To find the 8th term, substitute n = 8 into the equation for the nth term:

\(\implies a_8=2.8(8)+0.2=22.6\)

The number of different selections that a customer can make is of 210.

To calculate the number of different selections that the customer can make, we need to verify if the order of the selections matters or not, then:

In the context of this problem, the order does not matter, hence the combination formula is used.

The number of combinations, from a set of n elements, of x elements, is given according to the following rule:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, the number of selections is of 4 samples from a set of 10 samples, hence it is calculated as follows:

\(C_{10,4} = \frac{10!}{4!6!} = 210\)

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Answer:

200 students

Step-by-step explanation:

Since there are 7 buses and 6 of them are full you would multiply 30•6. Then you would multiply 2/3 with 30 to find how many are on the 7th bus, which is 20. So you would add 180 and 20 to get the answer

In this problem, we have two corresponding angles. (4x +28) and 116º

Since corresponding angles are congruent angles then we can state that:

4x +28 = 116 subtracting -28 from both sides

4x=116 -28

4x=88 Dividing both sides by 4

x= 22º

To solve this problem, we can use the method of Lagrange multipliers. This method allows us to find the maximum or minimum of a function subject to constraints.

In this case, the function we want to maximize is Z = 2x + 3y and the constraints are x = 24, y = 25, and 3x + 2y = 52.We begin by setting up the Lagrangian function, which is given by:L(x, y, λ) = Z - λ(3x + 2y - 52)where λ is the Lagrange multiplier. We then take the partial derivatives of the Lagrangian with respect to x, y, and λ and set them equal to zero.∂L/∂x = 2 - 3λ = 0∂L/∂y = 3 - 2λ = 0∂L/∂λ = 3x + 2y - 52 = 0Solving for λ, we get λ = 2/3 and λ = 3/2. However, only one of these values satisfies all three equations. Substituting λ = 2/3 into the first two equations gives x = 20 and y = 22. Substituting these values into the third equation confirms that they satisfy all three equations. Therefore, the maximum value of Z subject to the given constraints is Z = 2x + 3y = 2(20) + 3(22) = 84.

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The maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

To maximize the function Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, we will use the method of linear programming.

Let us first graph the equation 3x + 2y = 52.

The intercepts of the equation 3x + 2y = 52 are (0, 26) and (17.33, 0).

Since the feasible region is restricted by x ≤ 24 and y ≤ 25, we get the following graph.

We observe that the feasible region is bounded and consists of four vertices:

A(0, 26), B(8, 20), C(16, 13), and D(24, 0).

Next, we construct a table of values of Z = 2x + 3y for the vertices A, B, C, and D.

We observe that the maximum value of Z is 96, which occurs at the vertex B(8, 20).

Therefore, the maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

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The dominant strategy of Farmer Jones is to buy 10 cows.

To determine the dominant strategy of Farmer Jones, we need to compare the outcomes of his two options:

buying either 10 cows or 20 cows.

Let's analyze the potential outcomes for each case:

Buying 10 cows:

If Farmer Smith buys 10 cows:  

The total number of cows in the field would be 30, resulting in each cow producing $3000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

Buying 20 cows:

If Farmer Smith buys 10 cows:

The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.

If Farmer Smith buys 20 cows:

The total number of cows in the field would be 50, resulting in each cow producing less than $2000 of milk (exact value unknown).

From the given information, we can observe that regardless of the strategy chosen by Farmer Smith, Farmer Jones is better off buying 10 cows.

In all scenarios, the milk production per cow is higher when Farmer Jones buys 10 cows compared to buying 20 cows.

Therefore, the dominant strategy for Farmer Jones is to buy 10 cows.

Formally, we can express this as follows:

For Farmer Jones, no matter the strategy chosen by Farmer Smith, buying 10 cows yields a higher milk production per cow compared to buying 20 cows.

Hence, Farmer Jones' dominant strategy is to buy 10 cows.

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Your answer is 0.19.

I hope this helps you get a good grade on your test!!

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

I'm pretty sure the answer is 45 ft

Step-by-step explanation:

The string is out at all 80 feet, and is 35 feet away from a stop sign. Then wouldn't 80-35=45?

Answer:

The both on the right are the correct answers

Step-by-step explanation:

This is because rotational symmetry is defined as the property a shape has when it looks the same after some rotation by partial turns.