The Var (X) for the random variable X with probability density function
f ₓ(x) = Cx² for |x| ≤ 1 is equal to 3/5.
Probability density function (pdf) :
f ₓ(x) = Cx² for |x| ≤ 1
0 other wise
[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]
⇒ [tex]\int_{-1}^{1}Cx^{2}[/tex] = 1
⇒ C (x³ /3) [tex]|_{-1}^{1}[/tex] = 1
⇒ C/3 ( 1 - (-1 )) = 1
⇒(2/3) C = 1
⇒ C = 3/2
Now,
E(x) = [tex]\int_{-1}^{1}x (3/2)x^{2}dx[/tex]
= (3/2)[tex]\int_{-1}^{1}x^{3}dx[/tex]
= ( 3/2) ( x⁴ /4 ) [tex]|_{-1}^{1}[/tex]
= 0
Var (X) = [tex]\int_{-1}^{1}x^{2} (3/2)x^{2}dx[/tex] - [E(x)]²
= (3/2) [tex]\int_{-1}^{1} x^{4}dx[/tex] -0
= (3/2) ( x⁵ /5 )[tex]|_{-1}^{1}[/tex]
= (3/2 ) ( 1/5 + 1/5)
= 3/5
Therefore, the Var (X) of the probability density function for the random variable X is equal to 3/5.
Learn more about Var(X) here
brainly.com/question/15704115
#SPJ4
john builds cabinets. he makes $8.50 an hour, plus $3 extra for every cabinet he builds. last week he worked 36 hours and built 17 cabinets. how much money did he make?
John made at the end $357 for building cabinets
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
1 hour = 8.50$Extra = 3$/ cabinetWork = 36 hoursBuilt = 17 cabinetsTotal money = ?Total money will be as follow:
Total = 36*$8.50 + 17*$3
Total = $306+$51
Total = $357
Learn more about algebraic operations at: brainly.com/question/3927786
#SPJ4
cost price of a torchlight is rs.1400 its mp is 40% more than cost price if the shopkeeper sells it at 20% discount what is marked price of the torch
Answer:
The marked price of the torchlight is Rs. 1960.
Step-by-step explanation:
The marked price (MP) of a torchlight is 40% more than the cost price (CP), so we can calculate the MP using the formula:
MP = CP + (CP x 40%)
The cost price of the torchlight is Rs. 1400, so the marked price is:
MP = 1400 + (1400 x 40%) = 1400 + 560 = 1960
The shopkeeper is selling the torchlight at a 20% discount, so we can calculate the selling price (SP) using the formula:
SP = MP - (MP x 20%)
The marked price of the torchlight is Rs. 1960, so the selling price is:
SP = 1960 - (1960 x 20%) = 1960 - 392 = 1568
So the marked price of the torchlight is Rs. 1960.
Solve the following inequality, [tex]\frac{4a}{3}[/tex]≥ 2 ,representing each solution on a number line.
To solve the inequality, we need to get the variable on one side and the constant on the other side. We can start by multiplying both sides of the inequality by 3:
[tex]4a ≥ 6[/tex]
Now, we can divide both sides by 4:
[tex]a ≥ \frac{3}{2}[/tex]
The solution to this inequality is all values of a that are greater than or equal to 3/2. We can represent this on a number line as:
(-infinity, -1.5) U [1.5, infinity)
Where ( -infinity, -1.5) represents all values less than -1.5 and [1.5, infinity) represents all values greater than or equal to 1.5.
Note that the solution can also be represented as a >= 1.5.
Answer:
4a/3≥ 2
4a/3*3≥ 2*3
4a≥6
4a/4≥6/4
a≥3/2
On a number line, you would plot 3/2 with a filled in hole. The arrow you would draw to is the one that goes to the positive side, to the right. That's how to plot it.
Step-by-step explanation:
compute the complement 0.87
The complement of 0.87 is calculated by subtracting the given number from 1. Mathematically, this can be expressed as 1 - 0.87 = 0.13.
The complement of any number x is calculated by subtracting x from 1. This means that the complement of 0.87 is 0.13.
The complement of a number is used to find the remaining portion of a whole. For example, if the given number is 0.87, then the complement of 0.87 is 0.13. This means that 0.87 is 87% of the whole and 0.13 is the remaining 13%. Thus, the complement of 0.87 is 0.13.
Complements can also be used to find the probability of something happening. For example, if the probability of an event occurring is 0.87, then the probability of it not occurring is 0.13. This is because the sum of the probabilities must equal 1 (100%). Therefore, the complement of 0.87 is 0.13.
Learn more about complement of a number here:
https://brainly.com/question/21512303
#SPJ4
which of the functions in memory is more likely to be the interrupt service routine (isr) for handling system calls?
The functions in memory is more likely to be the Interrupt Service Routine (ISR) for handling system calls are f4 and f8
What is Interrupt Service Routine?
A software function known as an interrupt service routine (ISR) is called upon by hardware in response to an interrupt. An interrupt is examined by ISR, which decides how to handle it, executes the handling, and then returns a logical interrupt value. The ISR alerts the kernel with a return value if no more handling is necessary.
Reason:
Sending a Unix signal to the process that developed a variant allows for the handling of several variations. The intended action is delayed until the process receives a signal, allowing the kernel to evaluate other requests swiftly.
This approach does not accommodate interruptions since they typically occur after the associated process has ceased and the wholly unrelated process is running, as in the case of a process seeking a data transfer. Sending a Unix signal to the active process is therefore improper.
The handling of disruptions relies on the nature of interruption. We will categorize the three basic types of interruption for our needs as follows:
I/O causes disruptions.
The relevant interference handle should ask the I/O device to determine the best course of action if it needs attention. This kind of interruption is covered in the recently updated section "I / O Disorder Management."
Time is of the essence.
The kernel is informed that the deadline has passed by a specified timer, either an APIC timer or an external timer, by use of this type of interference. The majority of these illnesses are addressed as I/O disorders.
Another CPU multiprocessor system is interrupted by an interprocessor when its CPU is uninstalled. In the recently published section "Interprocessor Interrupt Handling," we conceal such interruptions.
Managing I/O Disruption
The I/O interfering adapter should typically be adaptable enough to support many devices simultaneously. For instance, many devices might share an IRQ line in the PCI bus architecture. This indicates that the interference vector alone does not provide a complete picture. The identical vector 43 is equipped with a USB port and sound card in the example displayed in Table 4-3. However, when their IRQ line is shared with other devices, several hardware components prevalent in earlier PC systems (such ISA) do not operate consistently.
The following list discusses two distinct methods for obtaining the bothersome handle's flexibility.
shared IRQ
Multiple interference lines are produced by the intrusion (ISRs). Each ISR is a feature connected to a single shared IRQ line device. Each ISR is carried out to see if its device requires attention because it is impossible to know in advance which device to issue an IRQ for. If it does, the ISR completes all the tasks that must be completed when the device generates interference.
When a disruption occurs, not all activities should be executed immediately. In actuality, not every activity should be performed near the distraction handle. Because the signals on the relevant IRQ line are momentarily disregarded while the interfering host is active, long-term non-processing performance should be delayed. Most crucially, even if system suspension is disabled, the disruptive host's process must continue in TASK RUNNING state. As a result, interference managers are unable to carry out any blocking operations like I/O disk performance. Linux divides post-disruption activities into the following three groups:
Actions that are crucial, such admitting PIC interference, redistributing the PIC or device controller, or updating the device's data acquisition and processor. Because it must be completed as soon as possible, this can be done rapidly and extremely swiftly. Sensitive actions are carried out when hidden interference is disabled inside the immediate disruption holder.
Not attentive
modifying data structures that are solely visible to the processor, for example (for example, reading a scan code after a push-key keyboard). These acts are turned into a short remedy with enabled distractions because they can also be swiftly stopped.
It is not indirectly transferred.
similar as replicating the bar's content in the process space (for example, sending the keyboard line bar to the end management process). Since the interested process will constantly be waiting for the data, this can be postponed for a long period without having an impact on kernel performance. The various tasks covered in the next section, "Softirqs and Tasklets," are used to carry out the actions that can be responded arbitrarily.
The functions f4 and f8 that handle system calls are more likely to be Interrupt Service Routines (ISRs) in memory.
To learn more about Functions visit:
brainly.com/question/28278699
#SPJ4
the perimeter of a square and rectangle are equal. if the sides of the rectangle are 12cm and 10cm,find the area of the square
Answer: The length of one side of the triangular-shaped walking path is 330 feet.
Step-by-step explanation:
The perimeter of the triangular-shaped walking path is 990 feet, and the length of one side is represented by x. We can write an equation to find x using the formula for the perimeter of a triangle:
P = a + b + c
Where P is the perimeter, and a, b, and c are the lengths of the sides of the triangle. Since one of the sides is represented by x, the equation can be written as:
990 = x + x + x
Simplifying the equation, we can find the value of x:
990 = 3x
Dividing both sides by 3, we get:
330 = x
So the length of one side of the triangular-shaped walking path is 330 feet.
what is the radius of the unit circle? 2) identify the sine, cosine and tan for either 30, 45, or 60 degrees in the 1st quadrant using exact values not decimal approximations. 3) what angle in each quadrant has the same reference angle as chosen in step 2? 4) how does the sine, cosine and tangent change in each quadrant for your chosen reference angle? 5) how do these changes relate to the coordinates on the unit circle in each quadrant?
The unit circle's radius is 1, that is 1 is the radius of the circle.
45 degrees' sine, cosine, and tan values are
[tex]sin \ 45^0=\frac{1}{\sqrt{2} }[/tex]
[tex]cos\ 45^0=\frac{1}{\sqrt{2 } }[/tex]
[tex]tan \ 45^0 =1[/tex]
Due to the fact that all angles are smaller than,
the reference angle coincides with the specified angle. In the first quadrant, 45 degrees is the reference angle, and sine, cosine, and tangent are all positive trigonometric functions.
In the second quadrant, sine is positive, cosine is negative, and tan is positive. In the fourth quadrant, sine and tan are negative, cosine is positive.
In the case of a unit circle, the cosine sine of the angle formed by the horizontal line is used to represent the unit circle's coordinates.
To learn more about Radius of circle :
https://brainly.com/question/11743473
#SPJ4
Given the quadratic function f(x)= 3x^2 - 2x + 5, calculate the average rate of change from x = -2 to x = 0.
The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.
what is function ?Qualities and their permutations, theorems and surrounding structures, morphologies and their placements, and locations where they can be encountered are all included in the study of mathematics. The association between a group of inputs, of which each has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a requires great, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on procedures, one-to-one functions, several more functions, within functions, and on functions.
given
The slope formula, (y2-y1)/, states that the average rate of change is the ratio of the change in y to the change in x.
(x2-x1) We have f(x), which is equivalent to byt but instead of y.
f(-2) - f (0) / -2
= f(14+4 + 5 ) + 5 / -2
28 / - 2
= -14
The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
The sum of the lengths of two adjacent sides of a rectangle is 16 cm and the length of a diagonal is 14 cm. Show that, when the breadth of the rectangle is taken as x cm, it satisfies the quadratic equation ² - 16x + 30 = 0, and find separately the length and the breadth of the rectangle to the first decimal place. (Use 5.83 for the value of √34.)
11. At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12
pounds. Let x represent how old the baby is in weeks and y represent the baby's weight in
pounds. Find the equation of the line that goes through these two points.
From given data, equation of line will be x - 2y = -16.
Find the equation of the line that goes through these two points?To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .
It's called this because it clearly identifies the slope and the y-intercept in the equation. The slope is the number written before the x. The y-intercept is the constant written at the end. Let's look at an example: y = 3x + 2.
Given,
x represent how old the baby is in weeks
y represent the baby's weight in pounds.
At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12 pounds.
⇒ (2,9)
⇒ (8,12)
Equation of line will be = y - yo = m (x - xo)
= y - 9 = 1/2 (x - 2)
= 2y - 18 = x - 2
= x - 2y = -16
To learn more about equation of line refers to:
brainly.com/question/18831322
#SPJ1
What is the slope of a line perpendicular to 10x + 4y = 20? a. −4
b. −4/10
c. −10/4
d. 10/4
e. 4/10
Correct option is E, The slope of a line perpendicular to y = -10/4 x + 5 is 4/10
What is the slope of a line perpendicular?The slope of the parallel line is undefined and the slope of the perpendicular line is 0.
Yes, the slope of a line perpendicular to the line 10x + 4y = 20 is indeed -4.
To find the slope of a perpendicular line, we can find the negative reciprocal of the slope of the original line.
The slope of line 10x + 4y = 20 can be found by solving for y and writing the line in slope-intercept form (y = mx + b), where m is the slope.
By solving for y in the equation 10x + 4y = 20:
10x + 4y = 20
4y = -10x + 20
y = -10/4 x + 20/4
y = -10/4 x + 5
So the line is in the form y = -10/4 x + 5, which is the slope-intercept form of a line where the slope (m) is -10/4 and the y-intercept (b) is 5.
Now, to find the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope of this line. The negative reciprocal of -10/4 is 4/10.
hence,. the slope of a line perpendicular to y = -10/4 x + 5 is 4/10
To learn more about the slope of a line perpendicular visit,
brainly.com/question/27589351
#SPJ4
if the simple interest on $800 for 3 years is $54, what is the rate of interest per annum
Answer:
The rate of interest per annum is 3%.
Step-by-step explanation:
The rate of interest per annum is 3%.
This can be calculated using the formula:
Simple Interest = (Principal x Rate x Time) / 100
In this case, we know that the Simple Interest = $54 and the Principal = $800, Time = 3 years.
So, we can rearrange the formula to solve for the Rate:
Rate = (Simple Interest x 100) / (Principal x Time)
Plugging in the given values, we get:
Rate = (54 x 100) / (800 x 3)
Rate = 3%
In circle F, the measure of ∠AFE is equal to 150° and the measure of arc BD is equal to 50°.
What is the measure of ∠C?
The measure of ∠C found using central angle and intercepted angle relationship is 50°.
What is central angle and intercepted arc of a circle?
An angle with its vertex at the circle's centre and both of its endpoints are on circle is said to be central angle. The angle's intercepted arc's ends are the same as the circle's endpoints. A circle's circumference includes an arc. Therefore, an intercepted arc is an arc that is created when one or more chords or line segments intersect a circle and come together at a vertex.
An important feature to remember when looking for missing arcs or central angles is that the angle measure of the central angle is equal to the measure of the intercepted arc.Given,
∠AFE = 150°
arc BD = 50°
External angle formed outside a circle,
= 1/2 ( major arc - minor arc )
Major arc = intercepted arc AE = central angle ∠AFE = 150°
Minor arc = arc BD = 50°
Therefore external angle ∠C = 1/2(150-50) = 50°
Hence 50° is the measure of ∠C.
To learn more about central angle and intercepted angle relationship, follow the link.
https://brainly.com/question/2487292
#SPJ1
in a lab experiment, a population of 300 bacteria is able to double every hour. which equation matches the number of bacteria in the population after 2 hours
The equation that matches the number of bacteria in the population after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and [tex]2^2[/tex] is the exponential term representing the doubling of the bacteria every hour.
In the lab experiment, the population of bacteria is doubling every hour, so after 2 hours, the number of bacteria will be 2 times the initial number of bacteria for each of the 2 hours, or [tex]2^2[/tex] times the initial number of bacteria.
So, the equation for the number of bacteria after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and 300 is the initial number of bacteria. This equation calculates the number of bacteria in the population after 2 hours by multiplying the initial number of bacteria by 2 raised to the power of the number of hours the bacteria has been doubling, or [tex]2^2[/tex] in this case.
Learn more about Simple Maths here:
https://brainly.com/question/30198551
#SPJ4
PLEASE HELP Find x and y.
The value of x and y in the given triangle is 4 and 6 respectively.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two triangles are similar. Using the rule of similar triangles we have:
4/ 6 = y / y+3
4(y + 3) = 6y
4y + 12 = 6y
12 = 2y
y = 6
Similarly, using the rule of similar triangles we have:
4/6 = x/6
(4)(6) = 6x
24 = 6x
x = 4
Hence, the value of x and y in the given triangle is 4 and 6 respectively.
Learn more about similar triangles here:
https://brainly.com/question/14926756
#SPJ1
Which one of the following functions is non-linear?
The function that is non-linear is (a) q = 8p³ + 9
How to determine the nonlinear functionFrom the question, we have the following parameters that can be used in our computation:
The list of options
As a general rule
Linear functions are functions with the highest power of 1
All but option (a) have a degree of 1
Hence. q = 8p³ + 9 is not linear
Read more about linear functions at
https://brainly.com/question/15602982
#SPJ1
because averages are less variable than individual outcomes what is true
The averages are less variable as compare to the individual outcomes is a true statement as individual value spread in wide range.
The averages are less variable compare to individual values.
It is a true statement.Average is the representation of the sum of all the individuals outcomes divided by number of individuals.Average is quiet near to all the individual values.Range of individual values to individual values is quiet wide compare to average to individual value.Spreading of data is more in individual values.Range of average is less than than individuals outcomes.Therefore, the individual values are more variable than averages is a true statement.
The given question is incomplete, I answer the question in general according to my knowledge:
Averages are less variable than individual outcomes is a true statement ? Give reason?
learn more about variable here
brainly.com/question/29583350
#SPJ4
Find the 12th term of the geometric sequence 2, 10, 50, ...2,10,50,...
the 12th term of the geometric sequence will be 97656250.
What is geometric sequence?
The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.
Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.
The terms are given 2,10,50...
a = 2
r = 10/2 = 5
The 12th term will be= 2*(5)[tex])^{11}[/tex] = 2 * 48828125= 97656250
Hence, the 12th term of the geometric sequence will be 97656250.
Learn more about the geometric sequence, by the following link
https://brainly.com/question/24643676
#SPJ1
consider the following quiz game. there are 2 questions. question 1 can be answered with probability 0.8 with reward $100 and question 2 can be answered with probability 0.5 with reward $200. if your first attempt in answering the question of your choice fails, the game is terminated. which question you should choose first to maximize your expected reward?
Question 1 should be chosen first to maximize your expected reward.
To maximize the expected reward, we need to calculate the expected reward for each question, taking into account the probability of getting the answer right and the reward for a correct answer.
For Question 1, the expected reward is 0.8 * $100 = $80, since you have an 80% chance of getting the answer right and earning a reward of $100.
For Question 2, the expected reward is 0.5 * $200 = $100, since you have a 50% chance of getting the answer right and earning a reward of $200.
Since the expected reward for Question 1 is higher than the expected reward for Question 2, you should choose Question 1 first to maximize your expected reward.
Learn more about expected value maximization;
https://brainly.com/question/10675141
#SPJ4
a van starts off 189 miles directly south from the city of hartville. it travels due west at a speed of 30 miles per hour. after travelling 126 miles, how fast is the distance between the van and hartville changing? (do not include units in your answer, and round to the nearest hundredth.)
The distance between the van and Hartville is changing at a rate of 39.42 miles per hour.
This is because the van has traveled 126 miles due west at a rate of 30 miles per hour, meaning it is now 63 miles away from Hartville. If the van continues travelling due west at a rate of 30 miles per hour, then it will take another 2 hours to reach Hartville. Thus, the distance between the van and Hartville is changing at a rate of 63 miles divided by 2 hours, or 39.42 miles per hour.
The distance between the van and Hartville is changing as the van travels due west at a rate of 30 miles per hour. After travelling 126 miles, the van will be 63 miles away from Hartville. This means that the distance between the van and Hartville is decreasing at a rate of 63 miles divided by the amount of time it takes for the van to reach Hartville, which is 2 hours.
Learn more about distance :
https://brainly.com/question/26550516
#SPJ4
Thoma ha 2. 10 pound of meat. He ue 0. 14 pound of meat to make one hamburger. How many hamburger can Thoma make with the meat he ha?
Thomas has 10 pound of meat. He used 0.14 pound of meat to make one hamburger, he can make 71 hamburger with the meat he has.
Thomas has in total 10 pounds of meat
In making one hamburger 0.14 pound of meat is used,
So the amount of hamburger made with the remaining meat is
10 - 0.14 = 9.86 pound
So, 9.86/0.14 = 70.42 ≈ 70.
So in total of 70 Hamburgers can be made with the meat Thomas has.
An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.
Learn more about Number of meat:
https://brainly.com/question/3166103
#SPJ4
Solve the equation
( attached an image of the problem)
Answer:
B
Step-by-step explanation:
[tex]x = \frac{2}{3}\pi r^{3}[/tex]
The objective is to isolate r and make r the subject of the equation:
Cross-multiplication is applied:
[tex]= 2\pi r^{3}= 3x[/tex]
The variables and number multiplied with [tex]r^{3}[/tex] are transferred to the other side of the equation:
[tex]= \pi r^{3} = \frac{3x}{2}[/tex]
[tex]= r^{3} = \frac{3x}{2\pi}[/tex]
Cube root is applied to both sides of the equation to get rid of the cube:
[tex]= \sqrt[3]{r^{3}} = \sqrt[3]{\frac{3x}{2\pi}}[/tex]
[tex]r = \sqrt[3]{\frac{3x}{2\pi}}[/tex]
36-30:[26-100:(10-12:b)=6
Answer:
36-30:[26-100:(10-12:b)]=6 - 10417845.
The line a intersects the y-axis at the same point as the line 11x + 3y + 6 = 0 and is parallel to the line 3x - y + 1 = 0.
a) Define the equation of line a
The equation of line a is given as follows:
y = 3x - 2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.The parallel line is defined as follows:
3x - y + 1 = 0.
In slope-intercept format, it is given as follows:
y = 3x + 1.
Hence the slope of line a is given as follows:
m = 3.
(as parallel lines have the same slope).
The intercept is the same as the line 11x + 3y + 6 = 0, hence:
3y + 6 = 0
3y = -6
y = -2
b = -2.
Hence the line a is defined as follows:
y = 3x - 2.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
what is the equation of the following line?(10,2)
Answer:
y=1/5x
That's the answer with the other point at (0,0)
Step-by-step explanation:
The function A() given by A()=0. 24551 can be ued to etimate the average age of employee of a company in the year 1981 to 2009. Let A() be the average age of an employee, and be the number of year ince 1981; that i, =0 for 1981 and =9 for 1990. What wa the average age of the employee in 2003 and in 2009?
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 ?
Learn more about Function here
https://brainly.com/question/14909799
#SPJ4
What is the discriminant of the quadratic equation 7x^2 - 13x - 5 = 0
A. 29
B. 309
C. -29
D. -309
Answer: B. 309.
Step-by-step explanation: The discriminant of the quadratic equation 7x^2 - 13x - 5 = 0 is D = b^2 - 4ac, where a = 7, b = -13, and c = -5.
Plugging in the values, we get:
D = (-13)^2 - 4 * 7 * -5 = 169 + 140 = 309
Therefore, the answer is B. 309.
Answer:B.309 I hope this helps you
Step-by-step explanation:
7x^2-13x-5=0
Identify the coefficients , and of the quadratic equation
something like this
a=7 b=-13, c=-5
Evaluate the discriminant by substituting a=7, b=-13 and c=-5 into the expression b^2-4ac
Something like this
(-13)^2-4 time 7( -5)
Simplify the expression then you get your answer
309
If you have $100, and you loe 1/2 of your remaining amount every week. How long will it take to get to 0?
If I lose half each week there is no value to reach "0" so we approximate the value to be less than 1, and the weekly amount is:
7 weeks
What is a fraction?Fractions are also called fractional numbers and are defined as an expressed numerical value that denotes a division and is expressed in the form:
x/y
Where:
x = numerator or dividing
y = denominator or divisor.
If the initial value we have is $100 and we determine its half, which is one week of expenses, we are left with the following:
$100 * 1/2 = $50
2nd week$50 * 1/2 = $25
3rd week$25 * 1/2 = $12.5
4th week$12.5 * 1/2 = $6.25
5th week$6.25 * 1/2 = $3.125
6th week$3.125 * 1/2 = $1.5625
7th week$1.5625 * 1/2= $0.78125
Learn more about fractions at:
https://brainly.com/question/28699958
#SPJ4
Use the Binomial Theorem and substitution to expand each Binomial. Show your step.
A) (3x+y)^4
B) (x-2y)^6
Answer:
A) (3x + y)^4:
The Binomial Theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n is given by the sum of n terms of the form:
C(n,k)a^(n-k)b^k
where C(n,k) is the binomial coefficient (n choose k).
So, expanding (3x + y)^4:
(3x + y)^4 = C(4,0)(3x)^4(y)^0 + C(4,1)(3x)^3(y)^1 + C(4,2)(3x)^2(y)^2 + C(4,3)(3x)^1(y)^3 + C(4,4)(3x)^0(y)^4
Using the binomial coefficients:
C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1
Expanding the terms:
(3x + y)^4 = 1(3x)^4(y)^0 + 4(3x)^3(y) + 6(3x)^2(y)^2 + 4(3x)(y)^3 + 1(y)^4
= 1(81x^4) + 4(27x^3y) + 6(9x^2y^2) + 4(3xy^3) + 1(y^4)
= 81x^4 + 108x^3y + 54x^2y^2 + 12xy^3 + y^4
B)
The Binomial Theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:
(a + b)^n = C(n, 0)a^n * b^0 + C(n, 1)a^(n-1) * b^1 + C(n, 2)a^(n-2) * b^2 + ... + C(n, n-1)a^1 * b^(n-1) + C(n, n)a^0 * b^n
where C(n, k) represents the binomial coefficient, which can be calculated as n! / (k! (n - k)!).
Applying this to (x - 2y)^6, we get:
(x - 2y)^6 = C(6, 0)x^6 * (-2y)^0 + C(6, 1)x^5 * (-2y)^1 + C(6, 2)x^4 * (-2y)^2 + ... + C(6, 5)x^1 * (-2y)^5 + C(6, 6)x^0 * (-2y)^6
Expanding each term:
C(6, 0) = 6! / (0! 6!) = 1
C(6, 1) = 6! / (1! 5!) = 6
C(6, 2) = 6! / (2! 4!) = 15
C(6, 3) = 6! / (3! 3!) = 20
C(6, 4) = 6! / (4! 2!) = 15
C(6, 5) = 6! / (5! 1!) = 6
C(6, 6) = 6! / (6! 0!) = 1
Now we can substitute each value into the equation:
(x - 2y)^6 = 1x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + 1 * (-2y)^6
Answer:
(x - 2y)^6 = x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + (-2y)^6.
Banana Republic at the Orlando, Florida, outlet tore ell caual jean for $45 and dre jean for $55. If cutomer bought 2 time more caual than dre jean and lat month’ ale totaled $4,060, how many of each type of jean were old?
The number of casual jeans sold was 81 and the number of dress jeans sold was 40.5 (rounded to 41).
Calculating Casual & Dress Jeans SoldLet's call the number of casual jeans sold "x". Then the number of dress jeans sold would be "x/2".The total revenue from the casual jeans would be $45 * x and the total revenue from the dress jeans would be $55 * x/2.We know that the total revenue was $4,060, so we can set up the following equation:$45x + $55x/2 = $4,060
Expanding the second term:$45x + $55x/2 = $4,060
$45x + $55x/2 = $4,060
$100x/2 = $4,060
$100x = $8,120
Dividing both sides by $100:x = 81
So from above calculation, we got that the number of casual jeans sold was 81 and the number of dress jeans sold was 81/2 = 40.5 (rounded to 41).
Learn more about Calculating Casual & Dress Jeans Sold here:
https://brainly.com/question/14434999
#SPJ4
