What is the simplified form of VT VVV ?

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

0

Step-by-step explanation:

to evaluate the composite function work from the inside out

first evaluate h(2) , then substitute the value obtained into g(x) then substitute the value obtained here into f(x)

h(2) = \(\frac{1}{2}\) , then

g( \(\frac{1}{2}\) ) = \(\sqrt{2(\frac{1}{2}) }\) = \(\sqrt{1}\) = 1 , then

f(1) = 1² - 1 = 1 - 1 = 0

Power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x=1.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

The given equation: \(\left(x^2-2 x+26\right) y^{\prime \prime}+x y^{\prime}-4 y=0\)

It is necessary to determine the power series solutions' minimal radius of convergence R around the typical points x = 0 and x = 1.

The separation between the ordinary point and the differential equation's singularity is now the minimal radius of convergence.

The polynomial's root, which is connected to the second derivative, is the singularity point.

The singularity points will be determined as follows:

\(\begin{aligned}& x^2-2 x+26=0 \\& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\& x=\frac{2 \pm \sqrt{(-2)^2-4 \times 1 \times 26}}{2} \\& x=1 \pm \sqrt{-100} \\& x=1 \pm 10 i\end{aligned}\)

In this case, x1 = 1+10i and x2 = 1-10i are the singularity sites.

The ordinary points at this time are z1 = 0+01 and z2 = 1+0i.

One can compute the minimum radius of convergence using the formula:

\(\begin{aligned}& r_1=\left|z_1-x_1\right| \\& =|0+0 i-1-10 i| \\& =\sqrt{101} \\& =10.0498 \\& r_2=\left|z_2-x_1\right| \\& =\sqrt{100} \\& =10\end{aligned}\)

Therefore, power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x = 1.

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The value of the double integral is 37.5, which represents the volume of the right triangular prism.

To identify the solid represented by the given double integral, we can rewrite the integrand in terms of the height of the solid at each point (x,y).

The integrand is (5 - x), which means that the height of the solid at point (x,y) is given by (5 - x). Therefore, the solid is a right triangular prism with a base in the xy-plane that extends from x=0 to x=5 and a height of 5 units.

The double integral can be evaluated by integrating the height function over the region R. Thus, we have:

∫∫R (5 - x) dA = ∫0^5 ∫0^3 (5 - x) dy dx

Integrating with respect to y first, we get:

∫0^5 ∫0^3 (5 - x) dy dx = ∫0^5 (5 - x) * 3 dx

= 3∫0^5 (5 - x) dx = 3(5x - x^2/2)|0^5

= 3(25/2) = 37.5

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The point is on second quadrant.

P(x, y) is on the unit circle

radius of the circle must be 1

The equation x² + y² = r²

\(y=\frac{2}{3}\), r =1

\(x^{2} (\frac{2}{3}) ^{2}= 1^{2}\)

\(x^{2} +\frac{4}{9} =1\)

\(x^{2} =1-\frac{4}{9}\)

\(x^{2} =\frac{5}{9}\)

\(x=\sqrt{\frac{5}{9} }\)

x = ±\(\sqrt{\frac{5}{9} }\)

x- c00rdinate is negative = - \(\sqrt{\frac{5}{9} }\)

P(x, y) = \((-\sqrt{\frac{5}{9} }, \frac{2}{3})\)

Therefore, the point is on second quadrant.

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Riley's mistake in step 2 of her homework was canceling out the x term in both the numerator and denominator of the second fraction. This cancellation is incorrect because the terms x and x-3 are not the same and cannot be simplified or canceled out.

To illustrate the correct simplification, let's evaluate the given expression:

\($$\frac{x}{x^2-5x+6} \cdot \frac{1}{\frac{x}{x-3}}$$\)

First, we simplify the denominator in the second fraction by multiplying by the reciprocal:

\($$\frac{x}{x^2-5x+6} \cdot \frac{x-3}{x}$$\)

Next, we notice that the x terms in the numerator and denominator of the second fraction can be canceled out:

\($$\frac{1}{\frac{1}{x-3}}$$\)

Further simplification can be done by multiplying the fraction in the denominator by its reciprocal:

\($$1 \cdot \frac{x-3}{1} = x-3$$\)

Hence, the correct simplification of the expression is x-3. Riley's mistake was canceling out the x terms in the second fraction, which led to an incorrect simplification.

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a) The elasticity is E(p) = (-800p)/((p + 6)^3 * D(p)).

b) The elasticity at p = 1, stating whether the demand is elastic, inelastic or has unit elasticity is E(1) = -114.29.

c) The value of p for which total revenue is a maximum is approximately $0.555.

a) To find the elasticity E(p) of the demand function q = D(p) = 400/(p + 6)^2, we can use the formula:

E(p) = (p/q) * (dq/dp)

where q is the quantity demanded, p is the price, and dq/dp is the derivative of q with respect to p.

Taking the derivative of the demand function with respect to p, we get:

dq/dp = (-800)/(p + 6)^3

Plugging this into the formula for elasticity, we have:

E(p) = (p/q) * (dq/dp) = (p/q) * (-800)/(p + 6)^3 = (-800p)/((p + 6)^3 * D(p))

where D(p) = 400/(p + 6)^2.

b) To find the elasticity at p = 1, we can substitute p = 1 into the equation for E(p):

E(1) = (-800*1)/((1 + 6)^3 * D(1)) = -114.29

Since the elasticity is negative, we know that the demand is inversely related to the price, meaning that as the price increases, the quantity demanded decreases.

To determine whether the demand is elastic, inelastic or has unit elasticity, we can look at the absolute value of the elasticity. Since |E(1)| > 1, the demand is elastic.

c) To find the value(s) of p for which total revenue is a maximum, we can use the formula for total revenue:

TR(p) = p * q = p * D(p)

Taking the derivative of TR(p) with respect to p, we get:

dTR/dp = D(p) - p * D'(p)

Setting this equal to zero to find the critical points, we have:

D(p) - p * D'(p) = 0

400/(p + 6)^2 - p * (-800)/(p + 6)^3 = 0

400/(p + 6) + 800p/(p + 6)^3 = 0

400(p^2 + 12p + 36) + 800p = 0

p^3 + 12p^2 + 16p - 36 = 0

This cubic equation can be solved using various methods, such as using the rational root theorem or using numerical methods. One solution is approximately p = 0.555, which corresponds to a maximum revenue.

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This reason why the area of the circle is more then 2 square units but less then 4 square units is: because, the circle does not totally cover the area defined by the four squares.

The area of a square is given by the formula;

Area = l²

Where l is side ength

Since each circle has area, A = 1 square unit.

Therefore,

Length of Each side of each square = 1 unit

This in turn is the radius of the circle given;

The area of the circle is therefore, Area = πr²

Area = (22/7) × 1²

Area = 3.142 square units

In conclusion the area of the circle is less than 4 square units.

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For given right triangles the value of a = 6√2 and b = 5/√3

In this question we have been given two right triangles.

In the first right triangle, we need to find the value of b.

Consider the tangent of angle 30°

tan(30°) = b/5

1/√3 = b/5

b = 5 × (1/√3)

b = 5/√3

In the second right triangle, we need to find the value of a.

This right triangle is isosceles right triangle.

So, the sides of right triangle are: a, 6, and 6

Using Pythagoras theorem,

a = √(6² + 6²)

a = √[2×(6²)]

a = 6√2

Therefore, for given right triangles the value of a = 6√2 and b = 5/√3

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Answer:73 ft

Step-by-step explanation:

Answer:

(120 + 12.5pi) ft^2

Step-by-step explanation:

10ft x 12 ft = 120ft^2

10ft/2 = 5 ft (Radius)

Area of semi circle:

\(\frac{\pi r^{2} }{2} = \frac{\pi 5^{2} }{2} = 12.5\pi ft^{2}\)

Area = (120 + 12.5pi) ft^2

Answer: 0.129 kg

Step-by-step explanation:

A gram to a kilogram can be found by dividing the value of grams by 1000, or multiplying the value by 0.001

The work required to raise the bucket and the remaining grain to the top is approximately 2,400 Joules.

To calculate the work required, we need to consider two components: the work required to lift the bucket and the work required to lift the remaining grain.

The work required to lift the bucket can be calculated using the formula:

Work_bucket = force_bucket * distance,

where force_bucket is the weight of the bucket and distance is the height it is lifted.

The weight of the bucket can be calculated as the product of its mass and the acceleration due to gravity:

Weight_bucket = mass_bucket * g,

where mass_bucket is the mass of the bucket (2 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values, we have:

Weight_bucket = 2 kg * 9.8 m/s^2 = 19.6 N.

The distance the bucket is lifted is 20 m.

Therefore, the work required to lift the bucket is:

Work_bucket = 19.6 N * 20 m = 392 J.

Next, we calculate the work required to lift the remaining grain. The weight of the remaining grain can be calculated in a similar way:

Weight_grain = mass_grain * g,

where mass_grain is the mass of the remaining grain (12 kg) and g is the acceleration due to gravity (9.8 m/s^2).

Substituting the values, we have:

Weight_grain = 12 kg * 9.8 m/s^2 = 117.6 N.

The distance the remaining grain is lifted is 10 m.

Therefore, the work required to lift the remaining grain is:

Work_grain = 117.6 N * 10 m = 1176 J.

To find the total work required, we add the work required to lift the bucket and the work required to lift the remaining grain:

Total work = Work_bucket + Work_grain = 392 J + 1176 J = 1568 J.

Therefore, the total work required to raise the bucket and the remaining grain to the top is approximately 2,400 Joules.

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When balloons filled to capacity outdoors at a temperature of 25∘F are brought indoors where the temperature is 70∘F, they will expand and increase in size as they warm up. The increase in temperature causes the air molecules inside the balloons to gain energy and move more rapidly.

When the balloons are brought indoors where the temperature is 70∘F, the air inside the balloons will begin to warm up. As the temperature increases, the air molecules inside the balloons gain energy and start to move more rapidly. This increased movement of the air molecules causes them to collide with the walls of the balloons more frequently and with greater force.

The collision of the air molecules with the walls of the balloons creates pressure inside the balloons. As the pressure increases, the balloons will start to expand and stretch. This expansion occurs because the rubber material of the balloons is flexible and can accommodate the increased volume of air.

As the balloons continue to warm up, the expansion will become more noticeable. The balloons will increase in size and become tauter. This happens because the air molecules inside the balloons are now occupying a larger space due to the increase in temperature. The rubber material of the balloons stretches to accommodate the greater volume of air.

It's important to note that if the temperature difference is significant, the expanding balloons may eventually reach their limits and could potentially burst if they are unable to withstand the internal pressure. Therefore, it's crucial to consider the temperature conditions when filling balloons to avoid overinflation.

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The solution for the matrix x in the equation Ax + 2B = C is

x = [[4/5, -9/10],

    [-6, -9/2]]

To solve for the matrix x in the equation Ax + 2B = C, we can rearrange the equation as follows:

Ax + 2B = C

Subtracting 2B from both sides:

Ax = C - 2B

To isolate x, we can multiply both sides by the inverse of matrix A (if it exists). Let's calculate the inverse of matrix A first:

A = [[5, 3], [5, 1]]

The determinant of A is:

|A| = (5 * 1) - (3 * 5) = -10

To find the inverse, we can use the formula:

A^(-1) = (1/|A|) * adj(A)

where adj(A) denotes the adjugate of A.

First, let's find the adjugate of A:

adj(A) = [[1, -3], [-5, 5]]

Now, we can calculate the inverse of A:

A^(-1) = (1/|A|) * adj(A) = (1/-10) * [[1, -3], [-5, 5]] = [[-1/10, 3/10], [1/2, -1/2]]

Next, we can multiply both sides of the equation by A^(-1):

A^(-1) * Ax = A^(-1) * (C - 2B)

Simplifying:

x = A^(-1) * (C - 2B)

Now we substitute the given matrices into the equation and perform the matrix operations:

A^(-1) = [[-1/10, 3/10], [1/2, -1/2]]

C = [[2, 4], [2, 5]]

B = [[5, 5], [2, 4]]

Calculating (C - 2B):

C - 2B = [[2, 4], [2, 5]] - 2 * [[5, 5], [2, 4]]

        = [[2, 4], [2, 5]] - [[10, 10], [4, 8]]

        = [[2-10, 4-10], [2-4, 5-8]]

        = [[-8, -6], [-2, -3]]

Now we can substitute the values back into the equation:

x = [[-1/10, 3/10], [1/2, -1/2]] * [[-8, -6], [-2, -3]]

Performing the matrix multiplication:

x = [[-1/10 * -8 + 3/10 * -2, -1/10 * -6 + 3/10 * -3],

    [1/2 * -8 + -1/2 * -2, 1/2 * -6 + -1/2 * -3]]

  = [[4/5, -9/10],

     [-6, -9/2]]

Therefore, the solution for the matrix x in the equation Ax + 2B = C is:

x = [[4/5, -9/10],

    [-6, -9/2]]

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Answer:

y=30

x=60

Step-by-step explanation:

The triangle has all sides equal therefore all the angles are equal.

For all the angles to be equal and add up to 180 (sum of angles in a triangle is 180), each angle has to be 60.

Therefore y=90-60

=30

x=180-(30+90)

=60

The relation is a function because it is a one-to-one relation

The relation is given as

y = -3x

The inputs are given as

x = 0, x = 1 and x = 2

Substitute the values of x i.e. x = 0, x = 1 and x = 2 in the equation of the function y = -3x

So, we have

y = -3(0) = 0

y = -3(1) = -3

y = -3(2) = -6

From the above computations, we can see that the y values are different for the inputs

Hence, the relation is a function because it is a one-to-one relation

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Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

----------------------------------------------------------------------------------------------------------------

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

----------------------------------------------------------------------------------------------------------------

Hope this helps! <3

Answer:

To find the leading coefficient, first expand the function:

\(y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14\)

The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².

To find the vertex: see image below

Vertex = (-3, -5)

Answer:

15 minutes

because 25% of 60 can be written as 25% × 60.

= 25/100 × 60

= 15

The digit in the one thousand place of the number 814,593 is "4".

In the number 814,593, the digit in the thousands place is "4".

To understand this, let's first review the place value system of numbers. Each digit in a number has a place value that depends on its position in the number. The rightmost digit is in the ones place, the digit to the left of that is in the tens place, and so on. The value of each place is 10 times the value of the place to its right. For example, in the number 814, the "4" is in the ones place, the "1" is in the tens place, and the "8" is in the hundreds place.

The thousands place is the next place to the left of the hundreds place, and its value is 10 times the value of the hundreds place. So, the digit in the thousands place of the number 814,593 is the digit that represents the thousands place value, which is "4".

Therefore, the digit in the one thousands place of the number 814,593 is "4".

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Answer:

Quadrant 3

Step-by-step explanation:

Since both x and y are negative, you go to the quadrant which has both negatives, meaning Q3

Answer:

I helped you with a previous question. So I got your pass.

Step-by-step explanation:

bla bla bla bla

have a great day!

Answer:

sry I am weak at gemotry..

Answer:

Same number of edges

Same number of angles

Angles woth same measures

Answer:

-80, -160, -320

Step-by-step explanation:

Answer: − 80 ,  − 160 , and  − 320

Step-by-step explanation:

From  − 5  to  − 10 , you multiplied by  2 . From  − 10  to  − 20 , you multiplied by  2 , and so on.

− 40  ⋅  2 = − 80  

− 80  ⋅  2  = − 160

− 160  ⋅  2 = − 320

Answer:  352(x)=1800

Step-by-step explanation:

Answer:

Evan can go on 30 rides   (based on the assumption that Evan's parent gave him $20)

Step-by-step explanation:

Given that:

The admission to the fair  = $5

The cost per ride = $0.50

Let assume that the number of ride Evan can go = x

So if The cost per ride = $0.50

x ride = $0.50x

We are not told that he is given money by anybody, but let assume his parent gave him $20,

Then, if Evan pays $5 for admission into the fair. Then he will have $(20-5) = $15 left

The relation expressing how many rides Evan can go is:

0.5x = 15

Since the cost per ride = $0.5

x rides cost $15/0.5

x = 15/0.5

x = 30

Hence, Evan can go on 30 rides

Answer: To write the equation of a line parallel to AB through a given point, we need to follow these steps:

Find the slope of the line AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1)/(x2 - x1)

Let the coordinates of points A and B be (x1, y1) and (x2, y2) respectively. Then, the slope of the line AB is:

m = (y2 - y1)/(x2 - x1)

Since we want to find the equation of a line parallel to AB, the slope of this line will also be equal to m.

Let the given point be (x0, y0). Using the point-slope form of the equation of a line, we can write the equation of the line passing through (x0, y0) with slope m as:

y - y0 = m(x - x0)

Substituting the value of m found in step 1, we get:

y - y0 = (y2 - y1)/(x2 - x1) * (x - x0)

This is the equation of the line parallel to AB passing through the point (x0, y0).

Note that we assume that the line passing through A and B exists and is not vertical. If the line is vertical, then its slope is undefined, and we cannot find the equation of a parallel line using this method. In that case, we need to use a different method to find the equation of the line.

Step-by-step explanation:

Answer:

4+2d

Step-by-step explanation:

2(3+d-1)

6+2d-2=6+(-2)+2d

=4+2d