Show that f (x) = x2 is continuous
at x0E IR for every x0E
IR.

So, the probability of winning the game by rolling a total of 2 or 5 with two fair number cubes is 1/9.

The probability of winning the game on your next turn by rolling a total of 2 or 5 with two fair number cubes is 1/9.

To calculate the probability of winning, we need to determine the number of favorable outcomes (rolling a total of 2 or 5) and divide it by the total number of possible outcomes when rolling two number cubes.

There are 36 possible outcomes when rolling two number cubes since each cube has 6 faces, resulting in 6 * 6 = 36 total outcomes.

Out of these 36 outcomes, there are three favorable outcomes: (1, 1), (1, 4), and (4, 1), where the sum of the numbers rolled is either 2 or 5.

Therefore, the probability of winning the game on your next turn is 3 favorable outcomes out of 36 possible outcomes, which simplifies to 1/12.

So, the probability of winning the game by rolling a total of 2 or 5 with two fair number cubes is 1/9.

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Answer:

18/42 or

36/84

Step-by-step explanation:

Answer: 3 to 7

Step-by-step explanation: Trust me i got 100.

Answer:

representative sample

Step-by-step explanation:

ik things

The option that is not a way by which minerals are being formed is decrystallization. That is option B

Minerals are organic substances that are form through the following ways;

Decrystallization is not a way through which minerals are formed because it is just the break down of solid or crystal structures.

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Complete question:

Which of the following is not a method by which minerals form?. a. crystallization. b. decrystallization. c. water evaporation from a solution. d. cooling of magma or lava

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Big boxes have 1/4 of 20 gigabytes of ram.

Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have

⇒ (1/4) x 20

⇒ 20 / 4

⇒ 5 gigabytes

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

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The corresponding square footage of the lawns that Derek mowed in the past five weeks is:

Week 1: 174,000 square feet

Week 2: 314,000 square feet

Week 3: 420,000 square feet

Week 4: 452,000 square feet

Week 5: 474,000 square feet.

To find the corresponding square footage of the lawns that Derek mowed in the past five weeks based on his earnings, we can use the given information about his charges and earnings.

Let's denote the square footage of lawn mowed as x and Derek's earnings in dollars as y. We know that Derek charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. This can be expressed as the equation:

y = 30 + (x/1000)

Now, we have the earnings (y) for the past five weeks: {204, 344, 450, 482, 504}. We can substitute these values into the equation and solve for x to find the corresponding square footage of lawn mowed.

For the first week: 204 = 30 + (x/1000)

174 = (x/1000)

x = 174,000 square feet

For the second week: 344 = 30 + (x/1000)

314 = (x/1000)

x = 314,000 square feet

For the third week: 450 = 30 + (x/1000)

420 = (x/1000)

x = 420,000 square feet

For the fourth week: 482 = 30 + (x/1000)

452 = (x/1000)

x = 452,000 square feet

For the fifth week: 504 = 30 + (x/1000)

474 = (x/1000)

x = 474,000 square feet

Therefore, the corresponding square footage of the lawns that Derek mowed in the past five weeks is:

Week 1: 174,000 square feet

Week 2: 314,000 square feet

Week 3: 420,000 square feet

Week 4: 452,000 square feet

Week 5: 474,000 square feet

These values represent the estimated square footage of lawn mowed based on the given earnings and the function that models Derek's charges.

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a) The percentage of students who failed the exam, given that they completed the exam review, is of: 15.38%.

b) The percentage of students who failed the exam, given that they did not complete the exam review, is of: 42.86%.

c) There is a negative association between failing the exam and completing the exam review.

A percentage is obtained by the division of the desired amounts by the total amounts, which is then multiplied by 100%.

For item a, these amounts are given as follows:

Hence the percentage is of:

p = 10/65 x 100% = 15.38%.

Then, for item b, the desired and total amounts are given, respectively, by:

Hence the percentage is obtained as follows:

p = 15/35 = 0.4286 = 42.86%.

Thus it can be concluded that there is a negative association between failing the exam and completing the exam review, as not completing the exam review makes you significantly likelier to not pass.

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Answer:

x+x+1+x+2+x+3+x+4

Step-by-step explanation:

5x+10 = 290

5x= 280

x = 280/5

x=56

least number is 56

Answer:

-8 < x< 3

Step-by-step explanation:

|2x+5| <11

there are two solutions, one positive and one negative ( remember to flip the inequality for the negative)

2x+5 <11  and   2x+5 > -11

Subtract 5 from each side

2x+5-5 < 11-5 and    2x+5-5 > -11-5

2x< 6           and           2x>-16

Divide by 2

2x/2 <6/2        and       2x/2 >-16/2

x <3                  and             x>-8

-8 < x< 3

x is less than 3 and x is greater than -8

open circles and -8 and 3 and a line between

Answer: true

Step-by-step explanation:

Answer: True

Step-by-step explanation: Has to be true if a b and c are all numbers

The pH of a weak acid solution can be calculated when it is titrated with a strong base.

1. Determine the initial concentration of the weak acid (Ha).

2. Calculate the dissociation constant (Ka) of the weak acid.

3. Calculate the initial concentration of the hydrogen ions (H+) in the solution. This can be done using the formula: [H+] = Ka * Ha / (1 + Ka).

4. Determine the amount of strong base added to the solution.

5. Calculate the amount of weak acid that has reacted with the strong base. This can be done using the equation: [Ha] = initial [Ha] - (base added * stoichiometry).

6. Calculate the new concentration of hydrogen ions in the solution after the reaction. This can be done using the formula: [H+] = Ka * [Ha] / (1 + Ka).

7. Calculate the pH of the solution after the reaction. This can be done using the formula: pH = -log[H+].

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Analyaze base line

2x+y=2

move x to other side

y=-2x+2

slope: -2

Pepindicular lines have negative reciprical slopes, so

-2 ---- 1/2

using point slope

y-3=1/2(x-2)

simplify

y-3=1/2x-1

move three to other side

y=1/2x-1+3

y=1/2x+2

Answer:

8.2FT

Step-by-step explanation:

Answer:

The answers 8.2!!

Step-by-step explanation:

I just guessed on the usatestprep and got it lol

Step-by-step explanation:

the area of the full larger circle minus the area of the smaller circle.

the area of a circle is

pi×r²

the radius of the smaller circle is 23.1 yd.

the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.

the area of the larger circle is

pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²

the area of the smaller circle is

pi× 23.1² = 1,675.5354 yd²

the area of only the ring around the smaller circle is then

2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈

≈ 1,322.57 yd²

or

pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =

= 421.2pi = 421.2 × 3.14 =

= 1,322.568 ≈ 1,322.57 yd²

The unit price of the clay pots is $1.39.

To find the unit price, we divide the total cost by the number of units.

In this case, the total cost of the 3-pack of clay pots is $4.17.

To find the unit price, we divide $4.17 by 3, which gives us $1.39.

Therefore, the unit price of the clay pots is $1.39.

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Answer:  The slope is \(\frac{2}{3}\).

Step-by-step explanation:

\(Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}\)

The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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The solution to the inhomogeneous Fredholm integral equations is:

a) Φₙ₊₁(x) = cos(x) + λ∫₀ˣ (\(e^x\))cos(t)Φₙ(t) dt

b) du(1)/dx - du(0)/dx + v(1) - v(0) = 0

To solve the inhomogeneous Fredholm integral equations of the second kind, we can use the method of iteration or the method of variation of parameters. Let's solve each equation separately:

(a) Φ(x) = cos x + λ∫0 to π (\(e^x\))costΦ(t) dt

To solve this equation, we'll use the method of iteration. Let's assume an initial guess for Φ(x) and iteratively refine it.

Step 1: Initial guess

Let's start with an initial guess Φ₀(x) = cos(x).

Step 2: Iteration

We'll use the formula for iteration:

Φₙ₊₁(x) = cos(x) + λ∫₀ˣ (\(e^x\))cos(t)Φₙ(t) dt

Iteratively, we'll refine our solution until it converges.

Step 3: Repeat iteration

Repeat Step 2 until the solution converges. In practice, you can choose a stopping criterion, such as a maximum number of iterations or a small change in the solution between iterations.

(b) Φ(x) = 1 + x² + λ∫₀ to 1 (x + t) Φ(t) dt

To solve this equation, we'll use the method of variation of parameters.

Step 1: Homogeneous solution

First, we'll solve the homogeneous equation by setting λ = 0:

Φ₀(x) = 1 + x²

Step 2: Particular solution

We'll find a particular solution using the variation of parameters.

Assume a particular solution of the form:

Φₚ(x) = u(x) + v(x)

where u(x) satisfies the homogeneous equation (λ = 0) and v(x) satisfies the inhomogeneous equation.

We differentiate Φₚ(x) with respect to λ and set it equal to the inhomogeneous term:

dΦₚ(x)/dλ = ∫₀¹ (x + t)(u(x) + v(x)) dt

Differentiating both sides with respect to x:

d²Φₚ(x)/dλdx = ∫₀¹ (u(x) + v(x)) dt + ∫₀¹ (x + t)(du(x)/dx + dv(x)/dx) dt

Setting this equal to the inhomogeneous term, we get:

∫₀¹ (u(x) + v(x)) dt + ∫₀¹ (x + t)(du(x)/dx + dv(x)/dx) dt = 1 + x²

Simplifying, we have:

∫₀¹ u(x) dt + x ∫₀¹ du(x)/dx dt + ∫₀¹ v(x) dt + x ∫₀¹ dv(x)/dx dt = 1 + x²

Integrating the second term by parts:

u(x) + x(u(1) - u(0)) + ∫₀¹ v(x) dt + x ∫₀¹ dv(x)/dx dt = 1 + x²

Setting the coefficient of x equal to zero:

u(1) - u(0) + ∫₀¹ v(x) dt = 0

Differentiating the above equation with respect to x:

du(1)/dx - du(0)/dx + v(1) - v(0) = 0

From these equations, we can determine u(x) and v(x). Once we have u(x) and v(x), we can find the particular solution Φₚ(x) = u(x) + v(x).

Correct Question :

Solve each of the following inhomogeneous Fredholm integral equations of the second kind for all values of λ for which there is a solution:

(a) Φ(x) = cos x + λ∫0 to π (e^x)costΦ(t) dt

(b) Φ(x) = 1 + x² + λ∫0 to 1 (x + t) Φ (t) dt

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VNTR analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats.

VARIABLE NUMBER TANDEM REPEAT (VNTR) analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats.

These tandem repeats consist of short DNA sequences repeated in a head-to-tail fashion.

VNTR analysis primarily focuses on identifying and characterizing the variations in the number of repeats within specific genomic regions.

By studying VNTRs, scientists can gain insights into genetic diversity, individual identification, and genetic relationships among individuals or populations.

VNTR analysis typically involves techniques such as polymerase chain reaction (PCR) amplification of the target region, followed by fragment analysis to determine the number of repeats present.

The variations in VNTRs make them highly polymorphic, meaning they differ significantly between individuals.

This polymorphism allows VNTR analysis to be used in various applications, including forensic analysis, paternity testing, population genetics, and evolutionary studies.

In summary, VNTR analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats, providing valuable information for genetic diversity and identification purposes.

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The distance between the middle school and the fire station is 4.5 miles

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

The distance between the middle school and the fire station is is the hypotenuse

therefore;

c² = 2² + 4²

c² = 4 + 16

c² = 20

c = √20

c = 4.5 miles(nearest tenth)

therefore the distance between the middle school and fire station is 4.5 miles

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Step-by-step explanation:

The answer is -9

Answer:

-9

Step-by-step explanation:

A Heaviside step function, frequently known as a step function, is a mathematical function that gives 0 for negative input and 1 for non-negative input. This function is represented by the symbol H(x) or u(x) and is useful in various scientific fields.

The step function was introduced by Oliver Heaviside in the year 1894. The Heaviside step function can be modified, scaled, shifted, and summed with other functions. The first example of the Heaviside step function is H(x) = 0 for x < 0 and H(x) = 1 for x ≥ 0.

The second example of the Heaviside step function is H(x - 2) which is a step function shifted by two units in the negative x-direction. The third example of the Heaviside step function is H((x + 3)/5) which is a step function shifted by three units in the positive x-direction and scaled by a factor of 5.

b) Solve the following differential equation: y'' + y = u(t-2), y(0) = 0 and y'(0) = 2, 0 ≤ t ≤ [infinity]i) The derivative property for Laplace transforms:Initial conditions of the second order differential equation y'' + y = f(t) can be solved by using Laplace transforms. We take the Laplace transform of both sides of the equation:

L(y'' + y) = L(f(t)).

By using the derivative property of Laplace transforms, we can write it as follows:

\(L(y'') + L(y) = L(f(t))s^2Y(s) - sy(0) - y'(0) + Y(s) = F(s).\)

By substituting the given values of initial conditions and the given Heaviside step function, we obtain:

\(s^2Y(s) - 2 = \frac{1}{s}e^{-2s}.\)

Solving this expression for Y(s), we get:

\(Y(s) = \frac{1}{s^3}e^{-2s} + \frac{2}{s^2}e^{-2s}.\)

Applying the inverse Laplace transform to Y(s), we obtain the solution of the given differential equation:

y(t) = \left(\frac{1}{2}t^2 - t + 1\right)u(t-2) - \left(t-2\right)u(t-2) + \left(1-t+e^{2-t}\right)u(t).

ii) The method of undetermined coefficients:In this method, the general solution of the given differential equation is found by assuming the solution of the forced part of the differential equation. For u(t - 2) = 1, we have:y'' + y = 1, y(0) = 0, y'(0) = 2The characteristic equation of the differential equation is:

r^2 + 1 = 0.

Solving this expression for r, we get:r = ±iThe homogeneous solution of the given differential equation is:

y_h(t) = c_1cos(t) + c_2sin(t).

The particular solution of the given differential equation is taken as:

y_p(t) = A.

Differentiating this expression with respect to t, we get:.

y'_p(t) = 0

y''_p(t) = 0.

Substituting these expressions in the given differential equation, we get:

y''_p + y_p = 1

0 + A = 1

A = 1.

Therefore, the particular solution of the given differential equation is:

y_p(t) = 1.

The general solution of the given differential equation is:

y(t) = c_1cos(t) + c_2sin(t) + 1.

Using the initial condition y(0) = 0, we get:

c_1 = -1.

Using the initial condition y'(0) = 2, we get:

c_2 = 2.

Therefore, the solution of the given differential equation is:

y(t) = 2sin(t) - cos(t) + 1.

For u(t - 2) = 0, the solution is the homogeneous solution y(t) = c1cos(t) + c2sin(t).

The Heaviside step function is a useful function in mathematics and science fields, and it can be modified, scaled, shifted, and summed with other functions. The Laplace transform and method of undetermined coefficients are used to solve the initial conditions of the given second-order differential equation.

The derivative property of Laplace transforms is used to solve the initial conditions of the differential equation. The method of undetermined coefficients is used to solve the given differential equation by assuming the solution of the forced part of the differential equation.

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Answer:

Angles 1 and 9 are corresponding angles

2 and 3 same side interior angles

8 and 12 are OTHER

6 and 12 are alternate interior

1 and 2 are linear pairs

15 and 11 are alternate interior

8 and 9 are same side interior

2 and 4 are corresponding

Step-by-step explanation:

Use the graph!

Brainliest??Hope it helped!

∠1 and ∠9 = Corresponding angles

∠2 and ∠3 = Same side interior angles

∠8 and ∠12 = Other

∠6 and ∠12 = Alternate interior angles

∠1 and ∠2 = Lineae pair

∠15 and ∠11 = Alternate interior angles

∠8 and ∠9 = Same side interior angles

∠2 and ∠4 = Corresponding angles

Let's use variables to represent the number of nickels and dimes: Let the number of dimes be x. The number of nickels is 19 more than dimes, or x + 19. We know that a collection of nickels and dimes is worth $2.90.

To write this as an equation, we can use the values of the coins in cents: 5x + 10(x + 19) = 290    Simplifying the equation:5x + 10x + 190

= 29015x + 190 = 29015x = 100x = 6.666...    The value of x should be a whole number, since we are counting coins. Since we can't have a fraction of a coin, we should round up or down to the nearest whole number. Since the value of x is closer to 7 than 6, we will round up.

x = 7Therefore, there are 7 dimes and 19 + 7 = 26 nickels.

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The flour that is needed is C. 3 and StartFraction 5 Over 12 EndFractioncups

The recipe calls for a total of 3 and two-thirdscups flour and sugar. If the recipe calls for One-fourthcup of sugar, the flour that will be needed will be:

= 3 2/3 - 1/4

= 3 8/12 - 3/12

= 3 5/12

Therefore, the correct option is C.

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