Find all the real zeros of the function. y=-1/8 (x-7)³-8 .

Answer:

2,4,5

Step-by-step explanation:

The length from 3rd base to 1st base is 127.3 ft

The correct answer is an option (H)

In this question,

A baseball diamond is a square with 90 -ft sides.

A baseball "diamond" is a square, each side of length 90 ft, with home plate and the three bases on the four corners.

Let s be the side length of the square.

The length from the 3rd base to 1st base  is the diagonal of the square.

Using Pythagoras theorem, we formulate

diagonal = √(s² + s²)

diagonal = √(2s²)

diagonal = s√2

diagonal = (90)√2

diagonal = 127.28 ft

Therefore, the length from 3rd base to 1st base is 127.3 ft

The correct answer is an option (H)

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The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Having a positive second derivative is beneficial because it indicates that the rate of change is increasing.

As input variable like interest rate, underlying stock price changes, rate of change in output variable like bond price, option price increases.

This can provide certain benefits, as discussed below.

Positive Convexity in Bonds,

Bond prices are inversely related to interest rates.

As interest rates increase, bond prices decrease and vice versa.

When a bond has positive convexity, its price will increase at an increasing rate.

As interest rates decline, and decrease at a decreasing rate as interest rates increase.

This is beneficial to bondholders.

Because it means that when interest rates decline, the bond's price will increase by more than it would if the bond had no convexity.

This can result in higher total returns for bondholders.

Long Gamma in Options,

Gamma is a measure of rate of change of delta the sensitivity of an option's price to changes in underlying asset price.

When an option trader is long gamma, it means they hold options that have positive gamma.

This is beneficial because it means that as the underlying asset price changes.

The option delta and therefore its price will change at an increasing rate.

Result in higher profits for the option trader especially if underlying asset experiences large price movements.

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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The ratios that are equivalent to 2:3 are:

6 to 9

8 to 12

To determine which of the given ratios are equivalent to 2:3, we need to simplify each ratio and check if they result in the same reduced form.

12 to 36:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 12:

12 ÷ 12 = 1

36 ÷ 12 = 3

The simplified ratio is 1:3, which is not equivalent to 2:3.

6 to 9:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 3:

6 ÷ 3 = 2

9 ÷ 3 = 3

The simplified ratio is 2:3, which is equivalent to 2:3.

8 to 12:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 4:

8 ÷ 4 = 2

12 ÷ 4 = 3

The simplified ratio is 2:3, which is equivalent to 2:3.

16 to 20:

To simplify this ratio, we can divide both terms by their greatest common divisor, which is 4:

16 ÷ 4 = 4

20 ÷ 4 = 5

The simplified ratio is 4:5, which is not equivalent to 2:3.

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The relationship between the points on the line and solutions to the linear equation is, the equation has a solution at each point along the line.

In the given question, we have to find the relationship between the points on the line and solutions to the linear equation.

The equation has a solution at each point along the line. This simply means that it is easy to tell whether an ordered pair is a solution to an equation. The ordered pair is a solution to the equation if it lies on the line drawn by the linear equation.

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Answer:

The y intercept is : 65

Step-by-step explanation:

The y intercept is 65 as it is in the form of y=mx+c.

The c is the y intercept, being 65

If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, Then the machine will take approximately 18 minutes to fill 240 bottles.

Constant rate is a rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Given that machine take 3 minutes to fill 40 bottles

So for 1 minute the machine fill \(\frac{40}{3}\) = 13.3333 bottles.

That is in 1 minute the machine fill approximately 14 bottles.

So the machine take a time to fill 240 bottles is \(\frac{240}{14} = 18.461\).

Thus the machine take approximately 18 minutes to fill 240 bottles.

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Answer:

your answer is in the screenshot cuz you didn't show the graph

Step-by-step explanation:

mrk me brainliest plz

Answer:

B. The frequency of temperatures throughout the day in Florida on April 25th.

Answer:

b) The frequency of temperatures throughout the day in Florida on April 25th

Step-by-step explanation:

The simplified expression of the perimeter of the triangle is 3.75x - 7.

A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The perimeter of a triangle is the sum of the whole three sides.

Therefore, the simplified expression that represents the perimeter of the triangle is as follows:

Hence, the three sides of the triangle are as follows;

Hence,

perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1

perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1

perimeter of the triangle = 3.0x + 0.75x - 7

perimeter of the triangle = 3.75x - 7

Therefore, the simplified expression is 3.75x - 7

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To show that Σ J₂(a) = Jo(√(a² - 2ax)), n! n=0, we need to use the properties of Bessel functions and their series representations.

First, let's start with the definition of the Bessel function of the first kind, Jn(x), which can be expressed as a power series:

Jn(x) = (x/2)^n ∑ (-1)^k (x^2/4)^k / k! (k + n)!

Now, let's focus on J₂(a). Plugging n = 2 into the series representation, we have:

J₂(a) = (a/2)² ∑ (-1)^k (a²/4)^k / k! (k + 2)!

Expanding the series, we get:

J₂(a) = (a²/4) [1 - (a²/4)/2! + (a²/4)²/3! - (a²/4)³/4! + ...]

Next, let's consider Jo(√(a² - 2ax)). The Bessel function of the first kind with order zero, Jo(x), can be expressed as a series:

Jo(x) = ∑ (-1)^k (x^2/4)^k / k!

Plugging in x = √(a² - 2ax), we have:

Jo(√(a² - 2ax)) = ∑ (-1)^k ((a² - 2ax)/4)^k / k!

Now, let's simplify the expression for Jo(√(a² - 2ax)). Expanding the series, we get:

Jo(√(a² - 2ax)) = 1 - (a² - 2ax)/4 + ((a² - 2ax)/4)²/2! - ((a² - 2ax)/4)³/3! + ...

Comparing the expressions for J₂(a) and Jo(√(a² - 2ax)), we can see that they have the same form of alternating terms with powers of (a²/4) and ((a² - 2ax)/4) respectively. The only difference is the starting term, which is 1 for Jo(√(a² - 2ax)).

To align the two expressions, we can rewrite J₂(a) as:

J₂(a) = (a²/4) [1 - (a²/4)/2! + (a²/4)²/3! - (a²/4)³/4! + ...]

Notice that this is the same as Jo(√(a² - 2ax)) with the starting term of 1.

Therefore, we have shown that Σ J₂(a) = Jo(√(a² - 2ax)), n! n=0.

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When events A and B are independent.

From the question, we have the following parameters that can be used in our computation:

P(A and B) = P(A) · P(B)

The above rule is used when the events A and B are independent events

This means that

The occurrence of the event A does not influence the occurrence of the event B and vice versa

Using the above as a guide, we have the following:

The correct option is (a)

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Answer:

$25

Step-by-step explanation:

Answer: k = √27-i

Step-by-step explanation:

9514 1404 393

Explanation:

The length CD can be found from the Pythagorean theorem.

  CF² + CD² = DF²

  2² + CD² = (2√10)²

  CD² = 40 -4 = 36

  CD = √36 = 6

From here, any of several methods could be used to find the area of ΔDEF.

One of them is to subtract the areas of the triangles that are not ΔDEF from the area of the rectangle ABCD.

  area ABCD = bh = (6 cm)(5 cm) = 30 cm²

  area ΔADE = 1/2bh = 1/2(4 cm)(5 cm) = 10 cm²

  area ΔBEF = 1/2bh = 1/2(2 cm)(3 cm) = 3 cm²

  area ΔCDF = 1/2bh = 1/2(6 cm)(2 cm) = 6 cm²

Then the area of interest is ...

  area ΔDEF = area ABCD -area ΔADE -area ΔBEF -area ΔCDF

  area ΔDEF = (30 -10 -3 -6) cm²

  area ΔDEF = 11 cm²

__

Alternate solution

If we define A as the origin of a coordinate system, then the coordinates of the vertices of ΔDEF are ...

  D(0, 5), E(4, 0), F(6, 3)

The area can be computed as half the absolute value of the sum of the determinants of 2×2 matrices consisting of adjacent points.

  \(A=\dfrac{1}{2}\left|\left|\begin{array}{cc}0&5\\4&0\end{array}\right|+\left|\begin{array}{cc}4&0\\6&3\end{array}\right|+\left|\begin{array}{cc}6&3\\0&5\end{array}\right| \right|\\\\=\dfrac{1}{2}|(0-20)+(12-0)+(30-0)|=\dfrac{1}{2}(22) = \boxed{11}\)

_____

Additional comment

The solution using coordinates is effectively equivalent to the computation of the area of trapezoid ABFD, less the areas of triangles EBF and AED.

So there are 6,840 possibilities to choose a committee of three students, one as president, one as vice president, and one as secretary.

As per the question given,  

We need to select 3 students from a class of 20, where order matters.

The number of ways to select the first student for the committee is 20, since we can choose any of the 20 students.

After selecting the first student, there are 19 students remaining to choose from for the second position (the vice-president). Once the vice-president is selected, there are 18 students remaining to choose from for the third position (the secretary).

Therefore, the total number of ways to select the committee is:

20 * 19 * 18 = 6,840

So there are 6,840 ways to select a committee of 3 students, where one student is the president, one is the vice-president, and one is the secretary.

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Greatest Integer Function [x] indicates an integral part of the real number.

The greatest integer of x, denoted as ⌊x⌋ or "the floor of x," refers to the largest integer that is less than or equal to x.

In other words, it rounds down x to the nearest whole number.

For example:

⌊3.7⌋ = 3: The greatest integer less than or equal to 3.7 is 3.

⌊-2.3⌋ = -3: The greatest integer less than or equal to -2.3 is -3.

⌊5⌋ = 5: Since 5 is already an integer, its greatest integer is itself.

The greatest integer function is useful when you want to simplify a real number to its nearest whole number without rounding up.

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Tenemos precio de lista de $25 para el libro.

Si aplicamos un descuento del 25%, este descuento representa:

Ahorramos $6.25.

El precio que pagamos el libro es $18.75.

Ok, so

If the scale from the real Eiffel Tower to the scale model is 15 ft to 3 in, the unit rate will be:

This means that, in the scale:

5 ft = 1 in.

Then, the unit rate is 5.

Answer:

6

Step-by-step explanation:

Let the required input be y.

\(h(y)=y-11=-5 \\ \\ y=6\)

We have expressed y in terms of the given expressions for a, b, c, and d. To simplify it further, we can distribute and perform the necessary computations.

To compute y = t^3 - 8 using the given expressions for a, b, c, and d, we need to substitute the values of a, b, and c into the expression and simplify it. Let's break it down step by step:

Given:

a = d - 1

b = d^2

c = d^2d - 2

d = d/dt

We can start by substituting d into a and b:

a = d - 1 = (d/dt) - 1

b = d^2 = (d/dt)^2

Next, we substitute the value of c:

c = d^2d - 2 = [(d/dt)^2][(d/dt)] - 2

Now, we substitute these expressions into y = t^3 - 8:

y = t^3 - 8

= (t^3 - 8)[(d/dt) - 1][(d/dt)^2][(d/dt)] - 2

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Answer:

Step-by-step explanation:

you could break up a term, like the y term.

x+2y+2y+9   this is equivalent

The derivative of the function f(t) = 3^(7t)/ t is 3^(7t)(7ln(3)t - 1) / t^2.  

Given function is f(t) = 3^(7t)/ t

To find the derivative of the function, we have to use the formula of quotient rule.

The formula is given as,If y = u/v, then dy/dx = (v du/dx - u dv/dx) / v²

f'(t) = [(t)(d/dt)(3^(7t)) - (3^(7t))(d/dt)(t)] / t^2

The first term requires the chain rule:

(d/dt)(3^(7t)) = (3^(7t))(d/dt)(7t) = (3^(7t))(7ln(3))

Substituting into the formula, we get:

f'(t) = [(t)(3^(7t))(7ln(3)) - (3^(7t))] / t^2

     = [3^(7t)(7ln(3))(t) - 3^(7t)] / t^2

Simplifying, we get:

f'(t) = 3^(7t)(7ln(3)t - 1) / t^2

Therefore, the derivative of the function f(t) = 3^(7t)/t is:

f'(t) = 3^(7t)(7ln(3)t - 1) / t^2

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Answer:

you have it correct sir

Step-by-step explanation:

Answer:

= 372,967

Step-by-step explanation:

hope it's help

#MASTER GROUP

# FIRST MASTER

# PHILIPPINES

Answer:

372967

Step-by-step explanation:

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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