You are stuck at home with your family during a quarantine. to pass time, you play games with your siblings lisa and maggie. in the course of 10 games, maggie wins all of them and you begin to suspect that she is cheating by rigging the dice. to check this, you roll two dice 200 times (observing the sum of the numbers facing up) that were being used for the games:

Answer:

The answer is d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The answer is C

use math

Answer:

3/4

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

(a) The probability distribution function (pdf) of X, the number of customers who paid by cash out of five randomly chosen, follows a binomial distribution with parameters n = 5 and p = 0.25.

(b) The probability that two or more customers out of five randomly chosen have paid by cash can be calculated by finding the complement of the probability that fewer than two customers have paid by cash.

(c) The standard deviation and mean of X can be determined using the formulas for the binomial distribution.

The pdf of X follows a binomial distribution because we have a fixed number of trials (five customers chosen) and each trial has two possible outcomes (either the customer paid by cash or didn't). The parameter n represents the number of trials, which is 5 in this case, and the parameter p represents the probability of success (a customer paying by cash), which is 0.25. Therefore, the pdf of X is given by the binomial distribution formula.

To determine the probability that two or more customers out of five have paid by cash, we can calculate the complement of the probability that fewer than two customers have paid by cash. We can find the probability of zero customers paying by cash and one customer paying by cash using the binomial distribution formula with n = 5 and p = 0.25. Subtracting this probability from 1 gives us the probability of two or more customers paying by cash.

The standard deviation of X can be calculated using the formula

\(\sqrt{(n * p * (1 - p))}\)

where n is the number of trials and p is the probability of success. In this case, n = 5 and p = 0.25. The mean of X can be calculated using the formula n * p.

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The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.

The given initial-value problem is a separable differential equation, which can be written as:

dy/dt = -2(t + 1)y²

Integrating both sides, we get:

(1/y) = t² + 2t  + C

where C is the constant of integration.

Since we have an initial condition, we can use it to find the value of C:

y(0) = -1/15
C = -1/15

Solving for C, we get:

C = -1/15

So, the solution to the differential equation is:

(1/y) = t² + 2t -1/15

y = 1 / (t² + 2t -1/15)

The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

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The radius of the ball, to the nearest hundredth, is approximately 10.63 cm.

To find the radius of the spherical ball, we'll use the formula for the surface area of a sphere, which is given by:

Surface Area = 4πr²

Given that the surface area of the ball is 452 cm², we can set up the equation:

452 = 4πr²

Dividing both sides of the equation by 4π, we get:

113 = r²

Taking the square root of both sides, we find:

r ≈ √113

Evaluating √113 to the nearest hundredth, we have:

r ≈ 10.63 cm

Therefore, the radius of the ball, to the nearest hundredth, is approximately 10.63 cm.

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The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Step-by-step explanation:

Sure, I'd be happy to help!

5 feet 7 inches is equivalent to 170.18 cm.

Answer:

B,AD

Step-by-step explanation:

BECAUSE I SAY IT

Answers:

x = -8/5 or x = 8/5

Sum of the first ten terms where all terms are positive = 4092

========================================================

Explanation:

r = common ratio

The first three terms are: 4, 4r, 4r^2

We're given that the sequence is: 4, 5x, 16

Therefore, we have these two equations

Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.

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

To find the sum of the first n terms, we use this geometric series formula

Sn = a*(1 - r^n)/(1 - r)

We have

So,

Sn = a*(1 - r^n)/(1 - r)

S10 = 4*(1 - 2^10)/(1 - 2)

S10 = 4*(1 - 1024)/(-1)

S10 = 4*(-1023)/(-1)

S10 = 4092

In summary, the given function \(f(x) = (e^(6x) - e^x) / (e^(3x) - e^(2(3x)))\) has no vertical asymptotes and no horizontal asymptotes.

To find the vertical and horizontal asymptotes of the function\(f(x) = (e^(6x) - e^x) / (e^(3x) - e^(2(3x)))\), we need to analyze the behavior of the function as x approaches positive or negative infinity.

First, let's determine the vertical asymptotes. Vertical asymptotes occur when the denominator of a rational function becomes zero. In this case, we need to find the values of x for which \(e^(3x) - e^(2(3x)) = 0.\)

\(e^(3x) - e^(6x) = 0\\e^(3x)(1 - e^(3x)) = 0\)

This equation is satisfied when either \(e^(3x) = 0\) or \(1 - e^(3x) = 0.\)However, since \(e^{(3x)\) is always positive, it can never equal zero. Therefore, there are no vertical asymptotes for the given function.

Next, let's determine the horizontal asymptotes. Horizontal asymptotes occur when the degree of the numerator and denominator of a rational function are equal. To find the horizontal asymptotes, we compare the degrees of the numerator and denominator.

The degree of the numerator is determined by the highest power of x, which is 6x. The degree of the denominator is determined by the highest power of x, which is 3x. Since the degree of the numerator (1st degree) is greater than the degree of the denominator (0th degree), there is no horizontal asymptote.

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To plot the line on a map, the length should be taken as approximately 120.3 ft, which is the horizontal component of the measured length along the sloping ground. Therefore, the correct answer is D. 120.3 ft.

To plot the line on a map, we need to find the horizontal component of the line's length. We can use trigonometry to calculate this.

The length of the line is 125.0 ft, and the angle of inclination between the horizontal and the ground is 15°44'. Let's denote the horizontal length as x.

Using trigonometry, we can find the horizontal component by taking the cosine of the angle:

Cos(15°44') = Adjacent / Hypotenuse

Cos(15°44') = x / 125.0 ft

Rearranging the equation to solve for x, we have:

x = 125.0 ft * Cos(15°44')

Calculating the value using a calculator, we find:

x ≈ 120.27 ft

Therefore, to plot the line on a map, its length should be taken as approximately 120.3 ft.

The correct answer is D. 120.3 ft.

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a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

We can approach this problem using the binomial distribution. Let X be the number of days in a week that the network crashes. Then X follows a binomial distribution with parameters n = 5 (number of days in a workweek) and p = 0.16 (probability of a crash on any given day).

a. The probability that the network crashes on both Monday and Tuesday is:

P(X = 2) = (5 choose 2) * (0.16)² * (1-0.16)³

= 0.1024

b. The probability that the network crashes for the first time on Thursday is the probability that it does not crash on Monday, Tuesday, or Wednesday, but does crash on Thursday and/or Friday. So:

P(X = 1) * P(no crashes on Monday, Tuesday, Wednesday) = (5 choose 1) * (0.16) * (1-0.16)⁴ * (0.84)³

= 0.3808 * 0.3652

= 0.1389

c. The probability that the network crashes every day is:

P(X = 5) = (5 choose 5) * (0.16)⁵ * (1-0.16)⁰

= 0.0001

d. The probability that the network crashes on at least one day is the complement of the probability that it does not crash at all during the week:

P(X >= 1) = 1 - P(X = 0)

= 1 - (5 choose 0) * (0.16)⁰ * (1-0.16)⁵

= 1 - 0.6778

= 0.3222

Therefore, a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.

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Answer:

beds in the hospital ≤ 47

Step-by-step explanation:

No more 47 means not greater than 47.

But can be = to 47 or less than it.

Answer:

(3x+2)^2+1

Step-by-step explanation:

(f°g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1

The required fog ( x ) = 3x² + 5. Option D is correct.

Given that,
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x) is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,
f( x ) = 3x + 2
g( x ) = x² + 1
fog ( x ) = f( g( x ) )
Same as substituting the value of x we substitute a function g inside the function f.
fog ( x ) = 3 (x² + 1) + 2
fog ( x ) = 3x² + 5

Thus, the required fog(x) = 3x² + 5. Option D is correct.

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The equation is already in standard form since standard form is

ax^2+bx+c = 0

Here we have

a = -3

b = 4

c = -2

The inverse of this function can be written as x=log(y/100)/log(1.05), where log is the natural logarithm (base e).

A function is a set of instructions that performs a specific task when called upon. It is a fundamental concept in programming languages that allows code to be written once and reused multiple times. Functions are used to break down complex tasks into smaller, more manageable pieces of code that can be tested and debugged independently. This modular approach to software development helps make code more efficient, easier to read and maintain, and less prone to errors. Functions can accept input in the form of parameters, or variables, and may optionally return a result.

This inverse function can be interpreted as the number of years it has taken for the cost per night at the hotel to reach a given value y. In other words, x represents the number of years since the hotel opened at which the cost per night is y.

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The logarithmic equation 2log4 - log3 + 2logx - 4 = 0 can be solved by rewriting the equation using logarithmic properties and then solving for x. The exact value of x depends on the logarithmic base used.

To solve the logarithmic equation 2log4 - log3 + 2logx - 4 = 0, we can start by applying logarithmic properties. Using the properties

log(a) - log(b) = log(a/b) and log(a^b) = b log(a), we can rewrite the equation as log(4^2) - log(3) + log(x^2) - log(10,000) = 0.

Simplifying further, we have 2 log(16) - log(3) + 2 log(x) - 4 = 0.

Next, we can combine the logarithmic terms using the property

log(a) + log(b) = log(a * b). This gives us log(16^2 * x^2 / 3) - 4 = 0. Simplifying the logarithm, we have log(256x^2/3) - 4 = 0.

To isolate the logarithm, we can apply the property a = b implies 10^a = 10^b. In this case,

10^(log(256x^2/3) - 4) = 10^0. This simplifies to 256x^2/3 = 10^4.

Finally, we solve for x by rearranging the equation. Multiplying both sides by 3/256, we get x^2 = (3/256) * 10^4. Taking the square root of both sides, we have x = ±√(3/256) * 10^2. Thus, the exact value of x depends on the logarithmic base used, but this provides the general form of the solution.

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The solutions (or roots) of 2x^2 + 8x + 26 = 0 are -2 + 3i and -2 - 3i.

To find the solutions of 2x^2 + 8x + 26 = 0, we can use the quadratic formula which states that for an equation of the form ax^2 + bx + c = 0, the solutions (or roots) are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 8, and c = 26. Substituting into the formula, we get:

x = (-8 ± sqrt(8^2 - 4(2)(26))) / 2(2)

Simplifying inside the square root:

x = (-8 ± sqrt(8^2 - 208)) / 4

x = (-8 ± sqrt(-144)) / 4

Since the square root of a negative number is not a real number, we can say that the solutions to this equation are complex numbers. Specifically, the solutions are:

x = (-8 + 12i) / 4 = -2 + 3i

x = (-8 - 12i) / 4 = -2 - 3i

Therefore, the solutions (or roots) of 2x^2 + 8x + 26 = 0 are -2 + 3i and -2 - 3i.

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Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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Answer: 0.25 inches per hour.

Step-by-step explanation:

The mile-a-minute weed can grow up to 0.5 ft per day. To convert this to inches per hour, we need to convert the distance from feet to inches and the time from days to hours.

There are 12 inches in 1 foot, so the mile-a-minute weed can grow up to 0.5 x 12 = <<0.5*12=6>>6 inches per day.

There are 24 hours in 1 day, so the mile-a-minute weed can grow up to 6 / 24 = <<6/24=0.25>>0.25 inches per hour.

Therefore, the mile-a-minute weed can grow up to 0.25 inches per hour.

Here's the complete solution using the correct conversion factors:

1 ft = 12 inches

1 day = 24 hours

0.5 ft/day * (12 inches/1 ft) / (24 hours/1 day) = 0.25 inches/hour

Answer:

<U=70

Step-by-step explanation:

Straight line=180 degrees

180-120

=60

So, we have 2 angles.

60 and 50

180=60+50+x

180=110+x

70=x

So, U=70

Hope this helps! :)

Answer:

36

Step-by-step explanation:

r = 3

b = 4

t = 7

\(\frac{red }{total}\) = \(\frac{red}{total}\)

\(\frac{3}{7}\) = \(\frac{r}{84}\)  Cross multiply

7r = 84(3)

7r = 252  Divide both sides by 7

r = 36

Answer:

=================

How many red roses did she sell?

Answer:

2500 roses are red.

Step-by-step explanation:

The numbers of 8 roses are,

→ r = 4000 ÷ 8

→ [ r = 500 times ]

Then amount of red roses are,

→ r × 5

→ 500 × 5

→ 2500 roses

Thus, answer is 2500 roses.

The exact value of tangent of 11 times pi over 12 is  \(-2+\sqrt{3}\).

We have to find the exact value of \(tan\frac{11\pi}{12}\)

\(tan\frac{11\pi}{12}=tan\frac{6\pi+5\pi}{12}\)

\(tan\frac{11\pi}{12}=tan(\frac{6\pi}{12}+\frac{5\pi}{12})\)

\(=tan(\frac{\pi}{2}+\frac{5\pi}{12})\)

We have \(tan(\frac{\pi}{2}+x)=-cotx\)

\(tan\frac{11\pi}{12}=-cot(\frac{5\pi}{12})\)

\(tan\frac{11\pi}{12}=-cot(\frac{2\pi+3\pi}{12})\)

\(tan\frac{11\pi}{12}=-cot(\frac{\pi}{6}+\frac{\pi}{4})\)

We have identity \(cot(x+y)=\frac{cotxcoty-1}{coty+cotx}\)

\(tan(\frac{\pi}{2}+x)= -\frac{cot\frac{\pi}{6}cot\frac{\pi}{4}-1}{cot\frac{\pi}{4}+ cot\frac{\pi}{6}}\)

\(=\frac{-\sqrt{3}(1) - 1}{1+\sqrt{3}}\)

Rationalize the denominator and simplify, we get:

\(=-2+\sqrt{3}\)

Therefore, the exact value of  \(tan\frac{11\pi}{12}\) is \(-2+\sqrt{3}\).

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Complete question is:

Find the exact value of  \(tan\frac{11\pi}{12}\) ?

Answer:

\(y = \frac{-2}{3}x + 2\)

Step-by-step explanation:

The first step is convert the given equation in a dependent and independent equation.

\(2x + 3y = 12\)

\(3y = 12 - 2x\)

\(y = 4 - \frac{2}{3}x\)

\(x\) is the independent variable and \(y\) the dependent variable.

Since both lines are parallel the slope of both equations are the same

\(y = \frac{-2}{3}x + b\)

Now for find the unknow \(b\) replace the \(x\) and \(y\) fo the given point.

\(4 = (\frac{2}{3})3 + b\)

\(4 = 2 + b\)

\(4 - 2 = b\)

\(2 = b\)

So the final equation is equal to

\(y = \frac{-2}{3}x + 2\)

The domain model class diagram is used to illustrate the domain models in object-oriented development. It provides an overview of a system's domain models, the major concepts, and their relationships.

These diagrams are used to give an understanding of the software system's requirements and to guide the system's design process.150 words:What is a domain model class diagram?A domain model class diagram is a type of UML diagram that is used to represent the domain models in object-oriented development.

This diagram is used to depict an overview of a system's domain models, the major concepts, and their relationships. A domain model is a visual representation of the system's domain, which includes the concepts, activities, and relationships between the concepts and activities.

A domain model class diagram can be used to capture the user's requirements and translate them into a software system.The domain model class diagram consists of classes, attributes, associations, and operations. Classes are the fundamental building blocks of the system and define the system's concepts.

Attributes are the properties of the classes, while operations are the actions that can be performed on the classes. Associations are the relationships between the classes, and they define how the classes are connected to one another.

The domain model class diagram provides a clear and concise representation of the system's domain and enables designers and developers to build software systems that meet the user's needs.

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