The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.
To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.
To illustrate, consider the system of equations:
x1 + x2 - x3 = 2
2x1 - x2 + 2x3 = 8
3x1 + 2x2 - 4x3 = 0
= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.
See more about existence and uniqueness at: https://brainly.com/question/30153142
#SPJ11
The manager at Braums recorded the orders of their customers over the last hour and had the following number of ice cream cones 4 vanilla, 5 chocolate, 2 peanut butter cup, 3 strawberry, and 2 coffee. Based on these numbers, what is the probability of the next customer ordering peanut butter cup? Write your answer as a decimal
Answer:
To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.
The total number of cones is:
4 + 5 + 2 + 3 + 2 = 16
The number of cones that are peanut butter cup is 2.
Therefore, the probability of the next customer ordering peanut butter cup is:
2/16 = 0.125
So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.
two cars leave the same parking lot, with one heading north and the other heading east. after several minutes, the northbound car has traveled 6 miles, and the eastbound car has traveled 8 miles. measured in a straight line, how far apart are the two cars?
The two cars are 10 miles apart, measured in a straight line.
We can use the Pythagorean theorem to find the distance between the two cars. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's imagine that the cars have traveled for some time, forming a right triangle where the distance between them is the hypotenuse. The northbound car has traveled 6 miles, which corresponds to the length of one of the legs of the triangle. The eastbound car has traveled 8 miles, which corresponds to the length of the other leg of the triangle. Therefore, the distance between the two cars is
distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles
Learn more about Pythagorean theorem here
brainly.com/question/14930619
#SPJ4
6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .
If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
To learn more about sample statistic link is here
brainly.com/question/29490427
#SPJ4
The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
A certain computer can perform a maximum number of operations per second. If this computer is running at 65%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 20 operations per second
2. 46 operations per second
3. 1,950 operations per second
4. 95 operations per second
Answer:
Let the maximum number of operations the computer can perform per second be x.
According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:
0.65x = 30
Solving for x, we get:
x = 30/0.65
x ≈ 46.1538
Rounding to the nearest whole number, we get:
x ≈ 46
Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.
eight different flavors are analyzed in a blind ice cream taste test. a participant is given four different ice cream samples and asked to sort them based on preference. in how many different ways can they be sorted?
There are 24 different ways that the participant can sort the four ice cream samples.
Since the participant is given 4 different ice cream samples, there are 4 ways in which they can place their first preference. Once they have chosen their favorite ice cream sample, there are 3 remaining options for their second preference. Similarly, there are 2 options for their third preference, and only one option for their least favorite ice cream sample. Here we have to use the principle of counting
Therefore, the number of ways the participant can sort the ice cream samples based on preference is
4 x 3 x 2 x 1 = 24
Learn more about principle of counting here
brainly.com/question/29594564
#SPJ4
Help! which environmental stimulus does a flatworm's eyespots detect?
distinct shapes around them
changes in light or dark
changes in movement
a wide variety of colors
Answer:
Changes in light and dark.
Step-by-step explanation:
I also do K12 loll
Changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.
What is Environment?A sum total of all the living and non-living elements and their effects that influence human life.
Flatworm's eyespots detect changes in light or dark in the environment. They are not capable of detecting distinct shapes or a wide variety of colors.
The eyespots are simple sensory structures that are used to detect the presence or absence of light and dark, and to detect changes in light intensity.
They are primarily used to help the flatworm locate and respond to light, which can be important for activities such as finding food or avoiding predators.
Hence, changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.
To learn more on Environment click:
https://brainly.com/question/30821114
#SPJ2
During a space shuttle launch, a maneuver is scheduled to begin at T minus 80
seconds, which is 80 seconds before liftoff. The maneuver lasts 1 1/2 minutes. At
what time will the maneuver be complete?
Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.
What is the order of rotation?The amount of rotations a shape can undergo around its center before returning to its initial position is referred to as the order of rotation in mathematics and geometry. It is also referred to as a shape's circular symmetry. A circle, for instance, has an order of rotation of infinite because it can be rotated indefinitely around its center without changing how it appears. A cube has an order of rotation of four because it will remain the same in shape whether it is rotated 90, 180, 270, or 360 degrees around its center.
given
At T minus 80 seconds, or 80 seconds prior to liftoff, the move is slated to start.
We must multiply the duration of the maneuver by the beginning time to determine the time at which it will be finished.
The move is estimated to take 1 and a half minutes. Since there are 60 seconds in a minute, we can change this to seconds by multiplying it by 60:
1 and a half minutes is equal to 1.5 minutes, 1.5 minutes multiplied by 60 seconds is equal to 90 seconds.
The move lasts 90 seconds as a result.
We multiply the duration of the move (90 seconds) by the start time (T minus 80 seconds) to determine the time at which the maneuver will be finished:
The move will be finished in T minus 80 seconds plus 90 seconds.
By adding the integers, we can make this simpler:
When the move is finished, the time will be T minus 80 seconds + 90 seconds + T plus 10 seconds.
Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.
To know more about the order of rotation visit :-
https://brainly.com/question/28485034
#SPJ1
what is the 1ooth digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 ?
The 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
First, let's convert the number (1 .fi.)3000 into its decimal representation. This is done by dividing 3000 by 10 raised to the power of the number of digits following the decimal point, which in this case is 3. We get the answer 1000, or 1.000.
Now, we can look at the 100th digit to the right of the decimal point. This will be the 0th digit from the right of the decimal point, which is 0. Therefore, the 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
Learn more about decimal representation:
brainly.com/question/12342812
#SPJ11
an individual was making blankets for some friends. the individual used 7.2 feet of fabric to make one blanket. how many feet of fabric will the individual need to make 11 blankets (round to the nearest whole number)?
The number of feet of fabric will the individual need to make 11 blankets is 79.2 feet
To find out how many feet of fabric the individual will need to make 11 blankets, we can use the unitary method.
We know that the individual used 7.2 feet of fabric to make one blanket. So, to find out how much fabric is needed to make 11 blankets, we can set up a proportion
7.2 feet of fabric is needed for 1 blanket
x feet of fabric is needed for 11 blankets
We can solve for x by cross-multiplying and then dividing
7.2 × 11 = x
x = 79.2 feet
Learn more about unitary method here
brainly.com/question/22056199
#SPJ4
HELP ASAP!!! What is the length of LN if the figure is a rectangle? (Attachment)
The length of the LN in the given rectangle is 33.
What is the intersection spot called?
The point of intersection is the location where two lines meet one another. If two straight lines are not parallel, they will eventually meet at some point. The meeting place of two straight lines is known as the point of intersection. The intersection location can be determined by simultaneously solving the equations for two straight lines that are passing.
In a rectangle, diagonals intersect at the right angle. The interesting point divides the lines into equal halves.
By solving the two equations, we can get the value of x.
LN = 4x-7
MO = 2x+13
Now, by equating two diagonal equations:
4x-7 = 2x+13
⇒4x-2x = 13+7
⇒2x = 20
⇒ x = 10
The required is LN = 4x-7
= 4(10) - 7
= 40-7
∴ LN = 33
To know more about Rectangle visit:
brainly.com/question/29123947
#SPJ1
What is the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less?The probability that the mean of a random sample of 52 pregnancies is less than 222 days is approximately ____. (Round to four decimal places as needed.)
The probability that the mean of a random sample of 52 pregnancies is less than or equal to 222 days is approximately 0.0005 (rounded to four decimal places).
Let's discuss it further below.
To solve the problem, we use the z-score formula, which is as follows:
z=(X−μ)/σX = sample mean = 222 days
μ = population mean = 226 days
σ = standard deviation of the population = 15 days
n = sample size = 52
To find the probability, we need to convert the sample mean to a z-score, which is calculated as follows:
z=(X−μ)/σ=(222−226)/(15/√52)=−4/2.096=−1.91
Now we need to find the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less, which is equivalent to finding the probability that a z-score is less than or equal to −1.91.
Using a z-table or calculator, we find that the probability of a z-score being less than or equal to −1.91 is approximately 0.0005 (rounded to four decimal places).
Therefore, the answer is 0.0005.
Learn more about probability.
brainly.com/question/30034780
#SPJ11
If a bus car 1km and 2 minutes what is the m/s
the speed of the bus in meters per second is 8.33 m/s. If a bus travels a distance of 1 kilometer in 2 minutes, we can use the formula for speed to calculate its speed in meters per second (m/s).
The formula for speed is:
Speed = Distance ÷ Time
Here, the distance is 1 kilometer, which is equal to 1000 meters (since 1 kilometer = 1000 meters), and the time is 2 minutes, which is equal to 120 seconds (since 1 minute = 60 seconds).
So, we can plug these values into the formula:
Speed = 1000 meters ÷ 120 seconds
Simplifying this expression, we get:
Speed = 8.33 meters per second (rounded to two decimal places)
Therefore, the speed of the bus in meters per second is 8.33 m/s.
To put this into context, it's important to understand that speed is the rate at which an object moves, while velocity is the rate at which it moves in a specific direction. So, in this case, we have only calculated the speed of the bus, not its velocity. However, knowing the speed of the bus can be useful for a variety of applications, such as determining how long it will take to travel a certain distance, or calculating the fuel efficiency of the vehicle
To know more about meters per second click here:
brainly.com/question/17894274
#SPJ4
PLEASE HELP ME ILL GIVE BRAINLIEST
Answer:
Please choose me please
Step-by-step explanation:
Answer:
The sample may be biased because the 50 people were selected at a local college baseball game, which could introduce selection bias. People attending a college baseball game may have different characteristics than the general population of the city, and therefore may not be representative of the population's opinions on the issue of building a new football stadium using tax funds. Additionally, the fact that they were selected at a baseball game may also introduce bias, as they may be more likely to be interested in sports and therefore more likely to support a tax-funded stadium. Overall, the sample may not be representative of the population's views, and therefore the conclusions drawn from the sample may not be generalizable to the entire population.
what is the slope of (1,-1) (4,8)
Answer:
The slope of the line passing through the points (1, -1) and (4, 8) is 3.
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the following formula:
[tex]slope = (y2 - y1) / (x2 - x1)[/tex]
Here, the given points are (1, -1) and (4, 8). So,
[tex]slope = (8 - (-1)) / (4 - 1) = 9 / 3 = 3[/tex]
Therefore, the slope of the line passing through the points (1, -1) and (4, 8) is 3.
we know the sample size is 90. for what sample proportion would the p-value be equal to 0.05? assume that all conditions necessary for inference are satisfied.
The sample proportion would be 0.5.we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.
To determine what sample proportion would yield a p-value of 0.05, we must first understand the formula for calculating a p-value. The formula for a p-value is p-value = 1 - [tex](1 - proportion)^n[/tex], where n is the sample size. By manipulating this equation, we can solve for the proportion when the p-value is equal to 0.05. We can isolate the proportion by taking the inverse of both sides of the equation, which yields: proportion = 1 - [tex](1 - 0.05)^(1/n)[/tex]. Since the sample size is 90, we can calculate the proportion by plugging in n = 90, which yields a proportion of 0.5.
Learn more about sample here
https://brainly.com/question/25894237
#SPJ1
I have been stuck on this question and I can't solve it.
Please help me!!
Answer:
Step-by-step explanation:
it is either Graph A or B pick one of them
Answer:
Graph D is correct
Step-by-step explanation:
if you choose a point, let's say 0,0 and plug in the values for x and y, you'll get
[tex]0 \leqslant - 2[/tex]
Since this equation isn't true, 0,0 can't be filled.
to choose between graphs c and d, you look at the line and because c is dotted, it means it isn't solution. because your sign is less than or equal to, the line has to be solid.
therefore, graph d is the correct answer
Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x = h + r cos(), y = k + r sin()
the parameter and obtain the standard form of the rectangular equation would be: [tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]
[tex]x=h+rcos\theta ,y=k+rsin\theta\\x-h=rcos\theta\\\frac{x-h}{r}=cos\theta...................(1)y=k+rsin\thetay-k=rsin\theta[/tex]
[tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]
square and add both the equations
[tex]\frac{(x-h)^2}{(r^2)} + \frac{(y-k)^2}{(r^2)} = sin^2\s\theta + cos^2\s\theta\\\\\frac{(x-h)^{2}}{r^{2}}+\frac{(y-k)^{2}}{r^{2}}=1\\\\ the value of (sin^{2}\theta+cos^{2}\theta=1)\\\\(x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
The overall rectangular (or standard) form of the perplexing numbers is a + b I. We can change over complex numbers in rectangular form, by tracking down r = a 2 + b 2 and θ = tan − 1 .
to know more about rectangular form click here:
https://brainly.com/question/30806916
#SPJ4
what is the average rate of change of f(x) from x = -3 to x = 6? f(x) = x^2 + 4x − 15 enter your answer in the blank.
The average rate of change of f(x) from x = -3 to x = 6 is 7.
What is meant by average?
The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.
To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.
For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:
[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]
The value of the function at [tex]x = 6[/tex] is:
[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]
The difference in the function values is:
[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]
The difference in the input values is:
6 - (-3) = 9
Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:
average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]
So, the average rate of change of f(x) from x = -3 to x = 6 is 7.
To learn more about average visit:
https://brainly.com/question/20118982
#SPJ1
Shirts are on sale for 30% off the oringal price of one shirt is 15 what is the total cost of 2 of these shirts at the sales price including a 7% sales tax
The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.
Original price of one shirt = $15
Number of shirts bought = 2
Sale discount = 30% off on original price
Sale price of one shirt = Original price - 30% of the original price
Substitute the value we get,
⇒Sale price of one shirt = 15 - (0.30)(15)
⇒Sale price of one shirt = $10.50
The cost of two shirts is equal to,
2 x $10.50 = $21.00
Sales tax = 7% of the total cost.
Substitute the value we have,
⇒Sales tax = 0.07 x $21.00
= $1.47
Total cost of two shirts = Cost of two shirts + Sales tax
⇒ Total cost of two shirts = $21.00 + $1.47
⇒ Total cost of two shirts = $22.47
Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.
Learn more about sales price here
brainly.com/question/30377864
#SPJ4
Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $450 and $550.
Answer: The probability is approximately 15.74%.
Step-by-step explanation: The probability that a worker selected at random makes between $450 and $550 can be found by standardizing the distribution of weekly wages using the formula:
z = (x - μ) / σ
where x is the weekly wage, μ is the mean weekly wage, and σ is the standard deviation of weekly wages.
Then we can use a standard normal distribution table or calculator to find the probability that a worker selected at random makes between $450 and $550.
Using this formula, we get:
z1 = (450 - 400) / 50 = 1
z2 = (550 - 400) / 50 = 3
The probability that a worker selected at random makes between $450 and $550 is equal to the probability that a standard normal random variable Z is between 1 and 3. This can be found using a standard normal distribution table or calculator.
Using a standard normal distribution table, we find that P(1 < Z < 3) = 0.1574.
Therefore, the probability that a worker selected at random makes between $450 and $550 is approximately 15.74%.
Hope this helps, and have a great day!
You have the option to pick between an action, horror, or
romantic comedy movie. You can also go at either 5pm, 7pm,
8pm, or 9pm. What is the total number of possible outcomes?
Find the center and radius of a circle with the equation x^2 + y^2 = 20.
x 2 + y 2 = 20
This is the form of a circle. Use this form to determine the center and radius of the circle.
( x − h ) 2 + ( y − k ) 2 = r 2
Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.
r = 2 √ 5
h = 0
k = 0
The center of the circle is found at ( h , k )
. Center: ( 0 , 0 )
These values represent the important values for graphing and analyzing a circle.
Center: ( 0 , 0 )
Radius: 2 √ 5
if you randomly draw a single coin out of the bag, what is the probability that you will obtain either a quarter or a nickel
Given how many coins are provided in the bag determines the chances for example of its a single nickel and a single quarter it'd be q50/n50 though if there's two nickels and one quarter there would be a n75/q25 chance.
if shoulders bought twice as many footballs as basketballs and the footballs cost $60 and the basketballs cost $30 and he spends $450, then how many footballs did he purchase?
Using equations, we can find that he purchased 6 footballs.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.
Here in the question,
Let the number of footballs purchased be f.
Let the number of basketballs purchased be b.
Cost of each football = $60.
Cost of each basketball = $30.
Total amount spent = $450
Now,
60f + 30b = 450
Given,
2b = f
⇒ b = f/2
Putting the value of b in the equation,
60f + 30(/2f) = 450
⇒ 60f + 15f = 450
⇒ 75f = 450
⇒ f = 6
Therefore, he purchased 6 footballs.
To know more about equations, visit:
https://brainly.com/question/29657983
#SPJ1
Choose the equation that represents the line passing through the point (2, −5) with a slope of −3
The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).
To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:
y - (-5) = -3(x - 2)
Simplifying this expression, we get:
y + 5 = -3x + 6
y = -3x + 1
Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.
Learn more about Slope:
https://brainly.com/question/16949303
#SPJ4
Complete Question:
Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.
A.) y = −3x − 13
B.) y = −3x + 11
C.) y = −3x + 13
D.) y = −3x + 1
Answer:
The answer is y = -3x + 1
Find the center and radius of a circle with the equation x^2 + y^2 = 20.
The given equation of the circle is:
[tex] \rm \: x^2 + y^2 = 20[/tex]
We can write this equation in standard form by completing the square:
[tex] \rm x^2 + y^2 = 20[/tex]
[tex] \rm x^2 + y^2 - 20 = 0[/tex]
[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]
[tex] \rm (x - 1)^2 + y^2 = 21[/tex]
Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.
The table below shows a set of points that have been dilated. The rule for the dilation is (x, y).
(x, y)
(0, 1)
(4,-2)
(-6,1)
True
False
Previous
(0,1)
(2,-1)
(-3,2)
O
Therefore, the table showing the original points and their corresponding dilated points is:
Original Point Dilated Point
(0,1) (0,1/2)
(4, -3) (2, -3/2)
(-6,1) (-3,1/2)
What is dilated point?I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.
To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.
given by the question.
To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.
Using this rule, we can find the dilated points for the given set of points as follows:
For the point (0,1), we have:
1/2x = 1/2 * 0 = 0
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (0, 1/2).
For the point (4, -3), we have:
1/2x = 1/2 * 4 = 2
1/2y = 1/2 * (-3) = -3/2
So, the dilated point is (2, -3/2).
For the point (-6,1), we have:
1/2x = 1/2 * (-6) = -3
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (-3,1).
To learn more about dilation:
https://brainly.com/question/13176891
#SPJ1
if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
To know more about cycle time refer here:
https://brainly.com/question/29669039
#SPJ11
A company has hired 14 new employees and must assign 10 to the dayshift and for to the Night Shift how many ways can the assignment be made ?
There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe
WHAT IS COMBINATION ?
Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.
To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:
C(n, k) = n! / (k! * (n - k)!)
where n! means n factorial (i.e. n multiplied by all the positive integers less than n).
In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:
C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))
Simplifying this expression, we get:
C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1
C(14, 10) * C(4, 4) = 1001 * 1
C(14, 10) * C(4, 4) = 1001
So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe
To know more about combination visit :-
https://brainly.com/question/11732255
#SPJ1
A rectangular yard measuring 29 ft by 45 ft is bordered (and surrounded) by a fence. Inside, a walk that is 4ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer
The walkway has a 656 square foot area.
An example of a measure is what?Comparing a quantitative measurement with a recognized standard amount of some kind is the act of measurement. For instance, in the measurement 10 kg, kg is indeed the basic measure used to describe mass of a physical quantity, and 10 is the size of the physical quantity.
In order to determine the size of the walkway, we must first determine the size of the bigger rectangle that includes the yard and the walkway, from which we must then deduct the yard's area.
The dimensions of the bigger rectangle will be:
Length: 29ft + 2(4ft) = 37ft
Width: 45ft + 2(4ft) = 53ft
Hence, the larger rectangle's area is:
37ft x 53ft = 1961ft²
The yard's actual size is:
29ft x 45ft = 1305ft²
As a result, the distinction between the two sections is the size of the walkway:
1961ft² - 1305ft² = 656ft²
Hence, the walkway has a 656 square foot area.
To know more about measure visit:
https://brainly.com/question/25716982
#SPJ1