20. Show that 2(1 – x)-'[(1 – x)-3+(1+x)-3] is the generating function for the number of ways to toss r identical dice and obtain an even sum.

Answer:

y - 2 = -2(x - 1)

Step-by-step explanation:

Point slope form is

y - y₁ = m(x - x₁)

where x₁ and y₁ are a point on the line

We are given (x₁, y₁)  = (1, 2) and m = -2

plugging in

y - 2 = -2(x - 1)

Answer:

56.........................

the curve length of C over the interval 0 ≤ t ≤ π/2 is (3π/2) units.

What is Parametric curve?

To find the curve length of the curve C defined by the parametric equations x = cos(3t) and y = sin(3t), where t ranges from 0 to π/2, we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t), where a ≤ t ≤ b, is given by:

\(L = ∫[a, b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt\)

Let's calculate the arc length for the given curve C:

x = cos(3t)

y = sin(3t)

First, we need to find the derivatives dx/dt and dy/dt:

dx/dt = -3sin(3t)

dy/dt = 3cos(3t)

Now, let's substitute these derivatives into the arc length formula:

\(L = ∫[0, π/2] √[ (-3sin(3t))^2 + (3cos(3t))^2 ] dt\)

\(L = ∫[0, π/2] √[ 9sin^2(3t) + 9cos^2(3t) ] dtL = ∫[0, π/2] 3 √[ sin^2(3t) + cos^2(3t) ] dtL = ∫[0, π/2] 3 dtL = 3[t] from 0 to π/2L = 3(π/2 - 0)L = 3π/2\)

Therefore, the curve length of C over the interval 0 ≤ t ≤ π/2 is (3π/2) units.

To know more about Parametric curve visit:

https://brainly.com/question/28498229

#SPJ4

The study outlined above is an experiment. In the study, two firefly colonies are set up in a laboratory environment and are subjected to different conditions. Therefore, it is an experimental design as the researcher is actively manipulating the independent variable which is the exposure of fireflies to light.

An observational study would involve recording data on a subject without manipulating their environment or situation. An observational study would have a less controlled environment in which the researcher does not interfere with the study subjects. There is a control group and a treatment group. The control group is the colony that is exposed to normal daylight/darkness conditions. The treatment group is the colony that is exposed to continuous light. The control group is used to provide a baseline measure or standard of comparison for the experiment.

It provides a way to compare the difference between the treatment group and the control group. Thus, the control group is the normal light/darkness colony, and the treatment group is the continuous light colony.

Know more about control group and a treatment group here:

https://brainly.com/question/29070427

#SPJ11

Answer: The correct equation to find the investment for the second year would be:

13,205 + x = 22,894

To solve for x, we subtract 13,205 from both sides:

x = 22,894 - 13,205

x = 9,689

Therefore, the investment for the second year is $9,689.

Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer  is option  (a).

A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.

The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.

a) They enable academics to investigate a theory's construct validity.

To know more about factorial design visit:

https://brainly.com/question/14053832

#SPJI

The amount of sales tax to be paid for the package at the resort is $26.39.

Sales tax refers to the amount to be paid to the governing body for a certain product or service.

Sales tax = cost of the service or product * \(\frac{Sales Tax Rate}{100}\)

Given:

The amount of sales tax to be paid =  \(754 * \frac{3.5}{100} = 26.39\)

Thus the amount to be paid at the resort for the package will be

= 754 + 26.39

= $ 780.39.

To learn more about sales tax and percentage, refer to the link:

https://brainly.com/question/9625982

#SPJ4

Answer:

ot would be the second and the third answer

Step-by-step explanation:

I'm just really good at them

Answer:

sss because we need an angle to solve using law of sines

Answer:

All you have is letters please repost so we can help you

Step-by-step explanation:

but this time put context

Answer:

60

Step-by-step explanation:

5/6 • 90/1 = 450/6 = 75

4/5 • 75/1 = 300/5 = 60

Answer:

60 houses left

Step-by-step explanation:

1/6 of 90 is 15, meaning 90 - 15 = 75 houses left

1/5 of 75 is also 15, meaning 75 - 15 = 60

60 are left

Please mark Brainliest, thank you!!

In order to identify these mentioned terms, it is important that each of them is defined.

Diameter: It is a line that passes through the center of the circle from one endpoint to another. It is two times the radius of the circle

Radius: It is a line drawn from the center of the circle to one endpoint of the circle.

It is half of the diameter.

Chord: It is a line drawn from one endpoint of the circle to another but does not necessarily pass through the center. Diameter is an example of a chord, but a chord does not have to be a diameter

Arc: It is a segment of the circumference of a circle

Circumference: is the total distance around the circle

From the diagram above:

|AB| is a diameter

|OA| or |OB| is the radius

|CD| is the chord

Arc CD is indicated on the diagram

If a circle has a radius of 2 cm:

Diameter = 2 x radius

Diameter = 2 x 2

Diameter = 4 cm

Therefore, if a circle has a radius of 2 cm, the diameter is 4 cm

Answer:

Step-by-step explanation:

The equation of the tangent line at theta = π/4 is y - 1/2 = x - 1/2. The arc length L of the parametric curve can be found by evaluating the integral of √[(dx/dt)^2 + (dy/dt)^2] over the interval [0, 2π]. The surface area A of the revolution generated by rotating the parametric curve about the x-axis can be found by evaluating the integral of 2πy√[(dx/dt)^2 + (dy/dt)^2] over the interval [0, 2π].

To find the equation of the tangent line at theta = π/4, we need to find the derivative dy/dx at that point.

dy/dx = (dy/dtheta) / (dx/dtheta) = (3sin^2θcosθ) / (3cos^2θsinθ) = tanθ.

Substituting θ = π/4, we have dy/dx = tan(π/4) = 1.

So, the equation of the tangent line is y - y0 = m(x - x0), where (x0, y0) is the point on the curve at θ = π/4.

Plugging in the values x0 = cos^3(π/4) = 1/2, y0 = sin^3(π/4) = 1/2, and m = 1, we get the equation of the tangent line as y - 1/2 = x - 1/2.

To find the arc length L of the parametric curve, we use the formula:

L = ∫[a,b] √[(dx/dt)^2 + (dy/dt)^2] dt, where [a, b] is the interval of theta.

Plugging in dx/dt = -3cos^2θsinθ and dy/dt = 3sin^2θcosθ, we have:

L = ∫[0, 2π] √[(-3cos^2θsinθ)^2 + (3sin^2θcosθ)^2] dθ.

Simplifying and integrating the expression, we can find the value of L.

To find the surface area A for the revolution generated by rotating the parametric curve about the x-axis, we use the formula:

A = 2π ∫[a,b] y √[(dx/dt)^2 + (dy/dt)^2] dt, where [a, b] is the interval of theta.

Plugging in dx/dt = -3cos^2θsinθ and dy/dt = 3sin^2θcosθ, we have:

A = 2π ∫[0, 2π] sin^3θ √[(-3cos^2θsinθ)^2 + (3sin^2θcosθ)^2] dθ.

Simplifying and integrating the expression, we can find the value of A.

To know more about equation,

https://brainly.com/question/31405534

#SPJ11

The two expressions that make up an equation or an inequality are connected in a mathematical statement.

How do you identify inequalities?

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.

A mathematical inequality is a comparison made between two algebraic expressions using the larger than (>), less than (), and other inequality symbols. An inequality pair connected by and or or is referred to as a compound inequality.

B. 3t + 3.5c <= 180 and 30t + 38c >= 1500.

The first inequality represents the constraint that the carpenter cannot work more than 180 hours in a month. The second inequality represents the requirement that they earn at least $1500 in a month.

These two inequalities, combined, describe the conditions that the carpenter must satisfy in order to manufacture tables and chairs in a way that meets both the time constraint and the income requirement.

To learn more about inequalities refer to:

brainly.com/question/24372553

#SPJ1

Solution

We want to reduce to lowest term

For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

To know more about probability,

https://brainly.com/question/18849307

#SPJ4

Answer:

f(x)=8x^3+6

y=8x^3+6 replace y and x

x=8y^3+6

x - 6=8y^3

(x - 6)/8=y^3

Step-by-step explanation:

a. If angle \( S U T \) is \( 39^{\circ} \), then the angle TUV is also \( 39^{\circ} \) because they are corresponding angles. Corresponding angles are pairs of angles that are in similar positions in relation to two parallel lines and a transversal, such that the angles have the same measure. Angle TUV is corresponding to angle SUT in this case.  The arc measure that describes arc \( V T S \) is \( 141^{\circ} \).  We can make assertions about these angle and arc measures by applying geometric principles such as the corresponding angles theorem and the arc measure formula. These principles allow us to establish relationships between angles and arcs based on their positions and measures.

b. Since we know that angle SUT is \( 39^{\circ} \) and angle TUV is corresponding to it, we can conclude that angle TUV is also \( 39^{\circ} \). This is an application of the corresponding angles theorem. Furthermore, we know that the sum of the arc measures of a circle is \( 360^{\circ} \), and that arc VTS is a minor arc that subtends the central angle TVS. Therefore, we can find the arc measure of arc VTS by applying the arc measure formula:

$$\text{arc measure} = \frac{\text{central angle}}{360^{\circ}} \times \text{circumference}$$

The central angle TVS is the same as angle TUV, which we know is \( 39^{\circ} \). The circumference of the circle is not given, so we cannot calculate the arc measure exactly. However, we know that the arc measure must be less than half the circumference, which is \( 180^{\circ} \). Therefore, we can conclude that the arc measure of arc VTS is less than \( 180^{\circ} \), but we cannot say exactly what it is.

In conclusion, by applying geometric principles such as the corresponding angles theorem and the arc measure formula, we can make assertions about the angle and arc measures in the given problem. We know that angle TUV is \( 39^{\circ} \) because it is corresponding to angle SUT, and we know that arc VTS has an arc measure that is less than \( 180^{\circ} \) based on the arc measure formula.

To know more about angle visit

https://brainly.com/question/30147425

#SPJ11

Let us consider the given zeros of the polynomial function i.e. `x = 2 + i` and `x = -7` to form linear factors for the polynomial function. We know that if a zero is given in the form `a + bi` then its conjugate is also a zero i.e. `a - bi`.

Hence, the linear factors of the given polynomial function are`(x - 2 - i)` and `(x - 2 + i)` for `x = 2 + i` and `(x + 7)` for `x = -7`Multiplying these linear factors we get, `P(x) = (x - 2 - i)(x - 2 + i)(x + 7)`After multiplying and solving the polynomial function we get.

Therefore, the polynomial function of minimum degree, with real coefficients, zeros at x = 2 + i and x = -7 and y-intercept at -140 is given by \[P(x) = x^3 - 11x^2 + 35x - 57\].

To know more about function visit :

https://brainly.com/question/30721594

#SPJ11

Answer:

61.56%

Explanation:

Let the first American = A

• P(A goes) = 0.62

• P(A does not) = 0.38

Let the second American = B

• P(B goes) = 0.62

• P(B does not) = 0.38

The probability that one or both of the people chosen does not go on vacation each year

=P(A goes and B does not) or P(A does not and B does) or P(both do not)

Therefore, the probability that one or both of the people chosen does not go on vacation each year is 61.56%.

Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

Learn more about Shamir secret

brainly.com/question/7473382

#SPJ11

Answer: either I don't understand the question or its 72% and I'm fairly certain its 72%

Answer:

Step-by-step explanation:

Because changing from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964.

The effect does have on the correlation of the two variables should be that it remain the same i.e. 0.964.

Since there is the changing from centimeters to meters so this does not impact the correlation value due to which it remain the constant i.e. 0.964.

Also, the correlation coefficient should be unit -less and the value should always ranged between -1 to 1.

Therefore, it remains the constant.

learn more about correlation here: https://brainly.com/question/1564293

The expression to show the best estimate is 64 * 2 +76 * 1

The given parameters are:

The expression to show the best estimate is

Expression = Gum package * Number of package + Candy bar * Number of bars

So, we have

Expression = 64 * 2 +76 * 1

Hence, the expression to show the best estimate is 64 * 2 +76 * 1

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

Both expressions equals to 32.

Step-by-step explanation:

You just plug in 5 for each expression: 12+4(5)=32, 4(5+3)=32.

Answer:

15, 3, -1, -12

Step-by-step explanation:

15, 3, -1, -12

Answer:

First answer (15, 3, -1, -12)

Step-by-step explanation:

ez

When a right triangle is rotated about one of its legs (assuming it's not the hypotenuse), it generates a solid known as a cone.

As the triangle rotates, the leg that acts as the axis of rotation sweeps out a circular base, while the other two sides of the triangle form the curved surface of the cone. The height of the cone is equal to the length of the leg being rotated. A triangular pyramid has a polygonal base with triangular faces meeting at a single vertex, which is not the case here. A cylinder has two circular bases, whereas a triangular prism has two triangular bases and three rectangular faces.

Therefore, the correct answer is: b) cone, when a right triangle is rotated about one of its legs (assuming it's not the hypotenuse).

To learn more about triangle click here: brainly.com/question/2773823

#SPJ11

The mean is μ=140.

The standard deviation is σ = 6.4807.

The probability that X (number of successful treatments) is 128 or less is 0.0322.

In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.

According to the question,

An allergy medication is successful in treating 70%

The medication is given to 200 patients.

Thus,

The random variable X is a binomial random variable with n = 200 (there were 200 patients).

The probability that a medication is successful in treating a randomly selected patient is 0.7.

p = 0.7 (the medication was successful in 70% cases).

Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.

\(\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}\)

Substitute values of 'n' and 'p' to get the result,

\(\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}\)

Thus, the mean is obtained as 140.

The standard deviation is 6.4807.

Step 2: find P(X≤128)

As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.

\($n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$\)

\(\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}\)

Therefore, the probability that X is 128 or less. is 0.0322.

To know more about the normal distribution, here

https://brainly.com/question/23418254

#SPJ4

The complete question is-

An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.

Answer:

1st. yes

2nd. no

i don't know

Step-by-step explanation:

The ladder touches the wall at a height of approximately 9.2 feet above the ground.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side, which is the ladder in this case) is equal to the sum of the squares of the lengths of the other two sides (the distance from the wall and the height of the ladder on the wall).

Let's call the distance from the wall "x" and the height of the ladder on the wall "h". Then we have:

\(x^2 + h^2 = 14^2\)

We also know that the bottom of the ladder is placed 3 feet from the wall, so we have:

x + 3 = 14

Solving for x, we get:

x = 11

Substituting this value into the first equation, we get:

\(11^2 + h^2 = 14^2\)

Simplifying and solving for h, we get:

\(h = \sqrt{(14^2 - 11^2)}\)

h ≈ 9.2

for such more question on word problem

https://brainly.com/question/1781657

#SPJ11