Let X denote a random variable that takes on any of the values -1, 0, and 1 with respective probabilities P(X= -1) = 0.2, P(X= 0) = 0.5, P(X = 1) = 0.3. Find the expectation of X.

Answer:

12.7 and 112.1

Step-by-step explanation:

|-12.7| and |112.1|, absolute value is distance from 0

Distance cannot be negative

Distance from 0 to -12.7 = 0 - (-12.7) = 0 + 12.7 = 12.7

Distance from 112.1 to 0 is 112.1 - 0 = 112.1

The converse of the conditional statement "If x < 20, then x < 30" is "If x < 30, then x < 20."

The converse statement is not true, because there are values of x that are less than 30 but are greater than or equal to 20.

Therefore, the counterexample is: x = 27.

If x = 27, the statement "If x < 30, then x < 20" is false because 27 is less than 30 but not less than 20.

Therefore, the answer is B) If x < 30, then x < 20 ; False -Counterexample: x=27 and x < 27.

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Answer:

16ft^2

Step-by-step explanation:

Room measures 6ft by 4ft. That means entire room floor measures 6 x 4 = 24 ft squared.

But a third of the room is taken up by the tub, toilet and sink. So only two thirds of the floor needs tiling.

24/3 = 8 (one third of the floor)

8 x 2 = 16 (Two thirds of the floor - place that needs tiling)

So the answer is 16 ft squared

Answer:

16ft^2

Step-by-step explanation:

6*4=24

1/3*24=8

8ft^2= toilet sink ect

24-8=16ft^2

Answer:

This is a RIGHT TRIANGLE.

Sure there are two acute angles, but if it was an acute triangle, then there should be three acute angles. It is not an obtuse triangle because there are no obtuse angles. This is a right triangle because there are two acute angles and there is a right corner, 90º. This is why this is a right triangle. It's quite simple.

The immigration agent is 100% busy on average.

Based on the information provided, we can calculate the arrival rate of entrants as follows:

Arrival rate = 1/6 minutes per entrant = 0.1667 entrants per minute

Next, we can calculate the processing rate of the immigration agent as follows:

Processing rate = 120 entrants per 8 hour shift = 0.05 entrants per minute

Using Little's Law, we can calculate the average number of entrants in the system as follows:

Average number of entrants = Arrival rate x Average time in the system

where Average time in the system = 1/Processing rate

Plugging in the values, we get:

Average number of entrants = 0.1667 x (1/0.05) = 3.333

Therefore, the immigration agent is busy with an average of 3.333 entrants in the system. To determine how busy she is as a percentage, we can use the following formula:

% utilization = (Average number of entrants / Number of servers) x 100%

In this case, there is only one immigration agent, so the number of servers is 1. Plugging in the values, we get:

% utilization = (3.333 / 1) x 100% = 333.3%

Since the maximum utilization cannot exceed 100%, the answer is 100%. Therefore, the immigration agent is 100% busy on average.

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Answer:

x ≤ -7

Step-by-step explanation:

There is a filled in circle which means that it is either ≤ or ≥.

The graph is going to the left, which means it is ≤

The starting number is -7.

x ≤ -7

There are 4²⁴ possible ways to complete the multiple-choice test consisting of 24 questions, with each question having four possible answers.

We have 24 questions with each having 4 possible outcomes. If we had a question, then we would have 4 ways of answering question 1 and for each of the four answers in question 1, we would have four ways of answering question 2. So, we have 4² ways of answering the questions.

Like this, we have 24 questions. There are four ways to choose an answer to each question. By counting principle, we multiply the number of choices at each step and then we have -

= 4×4×4×4...= 4²⁴ ways to complete the test

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If She can buy 5 sandwiches and have $3 in change or she can buy 2 sandwiches and have $9 in change then the cost of one sandwich is $4.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let's assume the cost of one sandwich to be 'x' dollars.

According to the problem, Jessie can buy 5 sandwiches and have $3 in change. This can be represented by the equation:

5x + 3 = total cost of 5 sandwiches with $3 change

Similarly, Jessie can also buy 2 sandwiches and have $9 in change, which can be represented by the equation:

2x + 9 = total cost of 2 sandwiches with $9 change

We can now solve these two equations to find the value of 'x', which represents the cost of one sandwich.

5x + 3 = 2x + 9 + 3

3x = 12

x = 4

Therefore, the cost of one sandwich is $4.

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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

Answer:

Step-by-step explanation:

Easy just divide this into 2 shapes.

The area of a rectangle is lenght Times Width.

2 Rectangles. So the One on the left would be

5X12=60 is the area of the first one.

The Second rectangle is

6X10=60

Both rectangles have the same area.

Now just add up both areas

60+60= 120 square units

SonicIsCoool, if you need more help I'm at your service

:)

Answer:

C. 120 units² or square units

Step-by-step explanation:

View the attached picture

Hope it helps!

The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer:

√(88×11×2×4}=√88²=±88 is your answer

Answer:

\(±88.\)

Step-by-step explanation:

\(= \sqrt{88 \times 88} \)

\( = \sqrt{ {88}^{2} } \)

\(±88\)

z can be 0. If A and B commute with each other, then they can be simultaneously diagonalized by a single matrix, say H. That is, there exists an invertible matrix H such that both H^(-1)AH and H^(-1)BH are diagonal matrices.

(a) False. z can be 0.

(b) False. The dimension of the generalized eigenspace for eigenvalue A is not necessarily equal to the number of linearly independent eigenvectors. In fact, there may be fewer linearly independent eigenvectors than the dimension of the generalized eigenspace.

(c) True. If A is a real positive matrix, then its eigenvalues are necessarily real numbers. This follows from the fact that any complex eigenvalue would imply the existence of a corresponding complex eigenvector, which in turn would lead to a contradiction since all entries of A are real and positive.

(d) True. By definition, p(A) is the determinant of the matrix (A - xI), where I is the identity matrix and x is a scalar variable. Since the determinant of a matrix is zero if and only if the matrix is singular, it follows that p(A) = 0.

(e) True. If A and B commute with each other, then they can be simultaneously diagonalized by a single matrix, say H. That is, there exists an invertible matrix H such that both H^(-1)AH and H^(-1)BH are diagonal matrices.

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Answer: im pretty sure its 14 divided by 79 soo 0.17?

if not im sorry

use your brain tho:)

hope this helps you

Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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Answer:

B

Step-by-step explanation:

hope this helps with the work

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }\)

Formula for the cylinder = V=πr2h

Formula for the cone = 1/3πr²H

Description:

So if the  cone and a cylinder have the same radius and the same height then it will be greater. So plug in these formula.

Formula:

Vcone = 3Vcone

Vcylinder = 360cm³

Vcone = 1/3 360cm³ = 120cm³

Answer: 120cm³

Hope this helps.

The bicycle tire needs an amount of 115 pumps to be fully inflated. (Correct choice: B)

In this problem we need to determine the number of pumps needed to inflate the bicycle tire at maximum pressure, this number (n) is equal to the maximum capacity of the tire (V), in ounces, and the mass added by a single pump (p), in ounces:

n = V / p

If we know that V = 640 oz and p = 5.6 oz (1 lb = 16 oz), then the number of pumps is:

n = 640 oz / 5.6 oz

n = 114.286

n = 115

An amount of 115 pumps are needed to inflate the bicycle tire to maximum pressure.

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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A n s w e r:

y = 8

Hope this helps!

Answer:

10x + 4

Step-by-step explanation:

Combine like terms.

First combine the numbers that have the letter x:

Then combine the ones that don't have the letter x

Answer is 10x+4

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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Remainder 11. We are aware that when a number is split by three, the remainder is created by dividing the digit sum by three. The law of three's divisibility asserts that a number is entirely divisible by three if the sum of its digits is also three-digit divisible.

If a polynomial f(x) is divided by xa, the result is the constant f(a) and f(x)=q(x)(xa)+f(a), where q(x) is a polynomial of degree one lower than f(x )'s.

The remainder theorem asserts that "when a polynomial of degree p(x) is divided by a linear polynomial of degree x - a, the remaining is p(a)" (OR) "when a polynomial of degree p(x) is divided by a linear polynomial of degree ax + b, the remainder is p(-b/a)".

The law of three's divisibility asserts that a number is entirely divisible by three if the sum of its digits is also three-digit divisible. We are aware that when a number is split by three, the remainder is created by dividing the digit sum by three.

The formula reads as follows: f(x)/x + 3.

A 0 x + 3 = 0 divisor should be used.

Calculate x x = -3.

The remainder of the quotient is 11.

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Based on the empirical rule, we would expect approximately 0.3% or 30 observations to lie beyond three standard deviations of the mean.

To explain further, the empirical rule, also known as the 68-95-99.7 rule, is a guideline that applies to data that follows a normal distribution. According to this rule, approximately 68% of the observations fall within one standard deviation of the mean, about 95% fall within two standard deviations, and roughly 99.7% fall within three standard deviations.

Since the normal distribution is symmetric, we can estimate that about half of the 0.3% of observations beyond three standard deviations would fall on each side of the mean. Therefore, we would expect around 0.3% / 2 = 0.15% of observations to lie beyond three standard deviations on each side.

To calculate the actual number of observations, we can multiply the percentage by the total sample size of 10,000. So, 0.15% of 10,000 is equal to 0.15 / 100 * 10,000 = 15.

Hence, we would expect approximately 15 observations to lie beyond three standard deviations of the mean in a sample of 10,000 from a normal population.

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a) The pmf of x is a geometric distribution,\(p(x) = (3/75)(72/75)^(x-1).\)

b) The expected number of bulbs tested until he gets a defective for the first time is 25.

a) The probability of success (getting a non-defective bulb) is 72/75 and the probability of failure (getting a defective bulb) is 3/75. The pmf of x is a geometric distribution, \(p(x) = (3/75)(72/75)^(x-1)\). This means that the probability of success P is multiplied by \((1-P)^(x-1)\) for each x value. b) The expected number of bulbs tested until he gets a defective for the first time is 25. This can be calculated as the sum of all x values multiplied by the corresponding pmf values: \(E(x) = Σ x p(x) = 3/75 + 24/75 + 48/75 + 72/75 + ... = 25\).

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Answer:

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

Step-by-step explanation:

This question can be solved using concept of LCM

LCM is the least number which is divisible by all the set of given number.

LCM is found by finding the prime factors of given set of numbers and then taking the each numbers highest power and then multiplying all.

for example

lets find LCM of 20 and 75

prime factor of 20 = 2*2*5

prime factor of 75 = 3*5*5

highest power of 2 is 2*2 = 4

highest power of 3 is 3 = 3

highest power of 5 is 5*5 = 25

thus LCM is 4*3*25 = 300

Thus, 300 is the least number which will be commonly divisible by 20 and 75.

Now in the problem given One light flashes every 18 seconds and another light flashes every 12 seconds.

Thus, they will will flast together at time when the time will be commonly divisible by both 12 and 18.

to find that time, lets find the LCM of 12 and 18

The number is 12 , 18

prime factor of 12 = 2*2*3

prime factor of 18 = 2*3*3

highest power of 2 is 2*2 = 4

highest power of 3 is 3*3 = 9

thus LCM is 9*4 = 36

Thus, the lights will flash together after 36 seconds.

Given that they flash together at 8:00 p.M

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

Given : jason wants to create a box with the same volume as the one shown

To find : measurements of width and height .

Solution :

Volume of given box

=> 6 * 2 * 3

=36

length to be 4 inches .

lwh = 36

=> 4 wh = 36

=> wh = 9

9 = 1 * 9

9 = 3 * 3

Width and Height can be 3 inches each or 1 and 9 inches