Answer:
AP = 29,37,45,...
d= t2-t1
=37-29
=8
n=59
t59=?
tn=a+(n-1)d
t59=29+(59-1)8
t59=28+58×8
t59=28 + 464
t59=492
Step-by-step explanation:
please mark it brainliest and thank it please
Can someone please help?
Answer:
5,1 and 9,-1 are the points
The earth's inner core is:
very dense
made of solid rock
hotter than the mantle
all of the above
none of the above
Answer:
Very dense...
Step-by-step explanation:
Answer :all of the above
Step-by-step explanation:
Question 2(Multiple Choice Worth 4 points)
(01.04 LC)
Given the linear functions f(x) = x -2 and g(x)=-3x + 4, determine (f- g)(x).
(f-g)(x) = -3x - 8
(f-g)(x)=-3x²-8
(f-g)(x) = -3x² + 10x - 8
(f-g)(x) = -3x² - 2x - 8
The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.
What is linear function?A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.
According to given information:To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).
The expression for (f - g)(x) can be found by subtracting g(x) from f(x):
(f - g)(x) = f(x) - g(x)
Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:
(f - g)(x) = f(x) - g(x)
= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]
= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]
= 4x - 6 [Combine like terms]
Therefore, (f - g)(x) = 4x - 6.
Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.
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i need to spend my points so
Answer:
Its 3 but why spend points?
Answer:
thanks hebehebebe Urdu itching frisk OCD bi ixixixixixiwjsnsbdbbddbbdbdbsbsjjzuhzhndj
X is a discrete variable, the possible values and probability distribution are shown as below
Xi 0 1 2 3 4 5
P(Xi) 0.35 0.25 0.2 0.1 0.05 0.05
Please compute the standard deviation of X
To compute the standard deviation of a discrete random variable X, we need to follow these steps:
Step 1: Calculate the expected value (mean) of X.
The expected value of X, denoted as E(X), is calculated by multiplying each value of X by its corresponding probability and summing them up.
E(X) = Σ(Xi * P(Xi))
E(X) = (0 * 0.35) + (1 * 0.25) + (2 * 0.2) + (3 * 0.1) + (4 * 0.05) + (5 * 0.05)
E(X) = 0 + 0.25 + 0.4 + 0.3 + 0.2 + 0.25
E(X) = 1.45
Step 2: Calculate the variance of X.
The variance of X, denoted as Var(X), is calculated by subtracting the squared expected value from the expected value of the squared X values, weighted by their corresponding probabilities.
Var(X) = E(X^2) - [E(X)]^2
Var(X) = Σ(Xi^2 * P(Xi)) - [E(X)]^2
Var(X) = (0^2 * 0.35) + (1^2 * 0.25) + (2^2 * 0.2) + (3^2 * 0.1) + (4^2 * 0.05) + (5^2 * 0.05) - (1.45)^2
Var(X) = (0 * 0.35) + (1 * 0.25) + (4 * 0.2) + (9 * 0.1) + (16 * 0.05) + (25 * 0.05) - 2.1025
Var(X) = 0 + 0.25 + 0.8 + 0.9 + 0.8 + 1.25 - 2.1025
Var(X) = 2.25
Step 3: Calculate the standard deviation of X.
The standard deviation of X, denoted as σ(X), is the square root of the variance.
σ(X) = √Var(X)
σ(X) = √2.25
σ(X) = 1.5
Therefore, the standard deviation of X is 1.5.
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-2x + y = 1
-4x + y = -1
Solve the following system of equation
Answer:
x = 2 and y = 5
Step-by-step explanation:
2x = 2
x = 2
-4 + y = 1
y = 5
true or false? "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g
The statement "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g is false because, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
Random assignment in an RCT can help to reduce selection bias, but it does not guarantee the absence of coverage bias.
Coverage bias can occur if the participants who are enrolled in the trial do not represent the population to which the results will be generalized.
For example, if the trial only includes participants who are healthier or more compliant than the typical patient, the results may not be applicable to the broader population.
Therefore, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
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Use the Distributive Property to simplify the expression. 8(s−1) =
Answer:
the answer would be 8s -8
Step-by-step explanation:
I learned this a long time ago
Answer:
anong grade Yan tol??g7 g7 g8 g9 g10 g11 g12?
Question included in file
please help I need an answer quick
The midpoint of the line AN is (3(1/2) , -1).
What is midpoint?
The midpoint is located halfway between the two end points. Its x and y values are in the middle of the two x and y values.Add both "x" coordinates, divide by 2, and add both "y" coordinates, divide by 2 to calculate it.Midpoint of the line(x , y) = (x₁ + x₂ / 2) , (y₁ + y₂ / 2)
x₁ = 2, x₂ = 5
y₁ = -3, y₂ = 1
So,
Midpoint of the line(x , y) = (2+5/2) , ((-3)+1 / 2)
= (7/2 , -2/2)
= (7/2, -1)
We can write 7/2 as 3(1/2)
Hence, the midpoint of the line AN is (3(1/2) , -1)
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100 POINTS !!!!!
Michael has a lunch account at the cafeteria. Michael can estimate the amount of money left in his lunch account using the equation y = 48 - 5x, where x represents the number of days he eats lunch. What is the meaning of the slope in the equation?
A. Michael has $48 in his lunch account.
B. Michael spends $5 per day eating lunch at the cafeteria.
C. Michael has $43 in his lunch account after eating one day.
D. Michael spends $10 of his lunch account after eating two days.
Answer:
B. Michael spends $5 per day eating lunch at the cafeteria.Step-by-step explanation:
Given linear equation:
y = 48 - 5xMeaning of each term is:
y - money left in account48 - the y-intercept, the intial amount of money in Michael's account- 5 - the slope, money spent every dayx - number of daysAccording to above details the correct answer choise is B
Answer:
b
Step-by-step explanation:
bc i did the schoolnet thingy
what is the midpoint of (0,0.55) and (-3,6)
Answer:
(-1.5, 3.275)
Step-by-step explanation:
midpoint = ( x1+X2/2 , y1+y2/2)
=(0+(-3)/2, 0.55+6/2)
=( -3/2, 6.55/2)
=( -1.5, 3.275)
1. Let f(x) = 2e4x-1
a. Show that f-1(x) = n(²7)+¹
4
in (²) +\
4
b. Write down the range of f -1.
In(-:-).
c. Solve the equation f (x) = In
Answer:3
Step-by-step explanation:
Step-by-step explanation:
Step-by-step explanation:
Step-by-step explanation:
A pregnant woman woke up and goes out of her room. She goes to the fridge and open a can of tuna, a soda, a yogurt and a cookie. What did she open first?
Answer:Well logically She opened the fridge door first!
Step-by-step explanation:
Her eyes too
There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 people use the gym and the pool. 29 people use the pool and the track. 25 people use the gym and the track. 11 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility
To find : Probability that person doesn't use any facility
Given : Total people = 130 ; People using gym (G), Swimming Pool (S), Track (T) = 73, 62, 58 respectively. People using G & P, P & T, G & T = 22, 29, 25. People using P & G & T = 11
So : Prob (G) = 73/ 130 , Prob (S) = 62/130 , Prob (T) = 58/130
P (G ∩ P) = 22 / 130 , P (P ∩ T) = 29 / 130 , P (G ∩ T) = 25 / 130 , P (P ∩ G ∩ T) = 11 / 130
Prob [ Person uses either P or G or T ] :
P (PUGUT) = P(G) + P (S) + P (T) - P (G ∩ P) - P (P ∩ T) - P (G ∩ T) - 2 P (P∩G∩T) = ( 73 + 62 + 58 - 22 - 29 - 25 - 22) / 130 = 95 / 130
Prob [Person uses neither P or G or T] : 1 - Pr [Person uses either P or G or T] = 1 - P (PUGUT) = 1 - (95 / 130) = 35 / 130
Hence, Probability that person doesn't use any facility = 35 / 130
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Answer:flying gorillla
Step-by-step explanation:because no
A cyclist rides a bicycle for hours at a constant speed of 12 miles per hour before taking a city bus 7 additional miles. If the cyclist
travels a total of 43 miles on the bicycle and the bus, which equation represents the number of hours the cyclist rides the bicycle?
The equation that represent the number of hours that the cyclist rides the bicycle is given as follows:
t = 36/3.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for this problem are given as follows:
v = 12 miles per hour.d = 36 miles -> total of 43 miles, 36 miles on the bicycle and 7 miles on the bus.Hence the equation that represent the number of hours that the cyclist rides the bicycle is given as follows:
t = 36/3.
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465 is what percent of 750?
Answer:
62
Step-by-step explanation:
A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected. Hence, the decision was to reject the null hypothesis retain the null hypothesis no decision was made.
a. True
b. False
Answer:
A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected. Hence, the decision was to retain the null hypothesis .
Step-by-step explanation:
A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected then the value of the test statistic is equal to zero.
Then the decision would be to retain the null hypotheses as zero is included in any value of the level of significance applied.
The chi square is a continuous distribution ranging from zero to plus infinity.
Please help! On my 2nd attempt again. '-'
Answer:
9?
Step-by-step explanation:
just try imputing number until you get the closet to what you need(Don't Take my answer as a fasho I haven't done this in a while
In Ehis emecius yose tunction will freeice four parameters. These parameters cortespond to stathitici far a baschall plaper's trading card. The tutction will use these paramesers for values in a dictlonary. The krys for each value are sone ited below. Finalic the function will frimen the dicfionary confructed wirhthese valums Function Name value__to_ded Parameters - at baca 1 an integer value (ley ia An - hisa l an inteser value (ier it ef\} - baeting average i float value (beria sval Return Value A detianary with the ken MS, 旦, Ma1, and A at. The values far each of these thould come from the irsut. parameters. Examples Exercise: values_to_dict Description In this exercise your function will receive four parameters. These parameters correspond to statistics for a baseball player's trading card. The function will use these parameters for values in a dictionary. The keys for each value are specified below. Finally, the function will return the dictionary constructed with these values. Function Name values_to_dict Parameters - at_bats : an integer value (key is AB) - hits : an integer value (hey is y) - runs_batted_in ; an integer value (key is RBI) - batting_average ia float value (key is AVG) Return Value A dictionary with the keys AB, H, RAI, and AVG. The values for each of these should come from the input parameters, Examples
These specifications match the data on a baseball player's trade card. The function will create a dictionary with keys for each of the supplied arguments ('AB', 'H', 'RBI', and 'AVG'). The function will finally return the built dictionary with the specified values for each key.
The `values_to_dict()` function will be implemented with four parameters corresponding to the statistics of a baseball player's trading card. The function will use these parameters for the values in a dictionary, and the keys for each value are provided below.Function Name: values_to_dictParameters:- `at_bats`: an integer value (key is AB)- `hits`: an integer value (key is H)- `runs_batted_in`: an integer value (key is RBI)- `batting_average`: a float value (key is AVG)Return Value: A dictionary with the keys AB, H, RAI, and AVG. The values for each of these should come from the input parameters.Example:Here's the function `values_to_dict()` implementation in Python:def values_to_dict(at_bats: int, hits: int, runs_batted_in: int, batting_average: float) -> dict:
# dictionary with keys and values
player_stats = {
"AB": at_bats,
"H": hits,
"RBI": runs_batted_in,
"AVG": batting_average
}
# return dictionary
return player_statsThe function will accept four parameters (`at_bats`, `hits`, `runs_batted_in`, and `batting_average`).
These parameters correspond to the statistics of a baseball player's trading card. The function will construct a dictionary with keys (`AB`, `H`, `RBI`, and `AVG`) and values for each of the given parameters. Finally, the function will return the constructed dictionary with the given values for each key.
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Which is the better buy? $6.48 for 18 ounce jar of peanut butter OR $5.28 for a 12 ounce jar of peanut butter. Explain your choice by giving the unit rate for each. *
Answer:
Hello! Your answer here is $6.48 for an 18oz jar of peanut butter. To determine which is the better buy, we can divide 6.48 by 18 and 5.28 by 12, which will give us the cost per ounce or unit rate. The $6.48 jar of peanut butter costs $0.36 per ounce, while the $5.28 jar of peanut butter costs $0.44 per ounce. The $6.48 jar of peanut butter is a better buy because it costs less per ounce.
Answer: $6.48 for 18 ounce jar of peanut butter is better to buy because its 0.36 dollars per ounce and the other one is 0.44 dollars per ounce.
Brainliest pleasee!!! :C
Jada has a meal in a restaurant. She adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00.
c) They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?
Answer: See explanation
Step-by-step explanation:
Your question wasn't well written but I saw an identical question so let me help out.
a. Jada has a meal in a restaurant she adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00. When the check comes, it says they also need to pay $3.99 in sales tax. what percentage of the subtotal is the sales tax?
b. They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?
a. Subtotal = $42.00
Tax = $3.99
Percentage of subtotal that is sales tax will be:
= Sales tax/Subtotal × 100
= 3.99/42.00 × 100
= 9.5%
b. Tip = $7
Sub total = $42
The percentage of the subtotal that is the tip will be:
= Tip/Sub total × 100
= 7/42 × 100
= 16.67%
Find the equation of the line shown.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-2}{4 +4} \implies \cfrac{ -2 }{ 8 } \implies - \cfrac{1}{4}\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{1}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -3 = - \cfrac{1}{4} ( x +4) \\\\\\ y-3=- \cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{4}x+2 \end{array}}\)
a box with a square base and an open top must have a volume of 4 m3 . find the height of the box that has the smallest possible surface area.
The height of the box that has the smallest possible surface area is 20m .
In the question ,
it is given that ,
the box has a square base ,
let the side of the box = "x" m
and let the height of the box = "y" m
volume of the box is given as 32000 m³,
So , x²y = 32000
y = 32000/x²
let the surface area of the box be "S" , that means
surface area(S) = area of base + total area of the 4 sides
= x²y + 4xy
Substituting the value of y = 32000/x² , we get
= x² + 4x(32000 / x²)
= x² + 128,000 / x, x > 0
to minimize the area we differentiate it with respect to x,
we get ,
= 2x - 128,000 / x²
= (2x³ - 128,000) / x²
Substituting S' = 0 , we get , 2x³ = 128,000
x³ = 64,000
x = 40
and y = 32000/(40)² = 20 m .
Therefore , The height of the box that has the smallest possible surface area is 20m .
The given question is incomplete , the complete question is
A box with a square base and open top must have a volume of 32,000 m³ . Find the height of the box that has the smallest possible surface area ?
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What is the upper quartile, Q3, of the following data set? 42, 38, 30, 53, 54, 66, 27, 61, 31, 57, 46, 18, 35, 49, 23
The upper quartile, Q3, of the given data set, is 54.
The upper quartile, Q3, is a measure of central tendency that represents the 75th percentile of a given dataset. It divides the data into two halves, with the upper half representing the range of values from Q3 to the maximum value. In order to find the upper quartile, we first need to arrange the data set in ascending order: 18, 23, 27, 30, 31, 35, 38, 42, 46, 49, 53, 54, 57, 61, 66.
Next, we need to determine the position of Q3 in the dataset. Since there are 15 data points in the set, Q3 will be located at the 75th percentile or 11.25th data point. To find the exact value of Q3, we can use the following formula:
Q3 = (0.75 * (n + 1)th term) + (0.25 * (n)th term)
where n is the number of data points in the set. Substituting the values, we get:
Q3 = (0.75 * 16th term) + (0.25 * 15th term)
Q3 = (0.75 * 12) + (0.25 * 11)
Q3 = 9 + 2.75
Q3 = 11.75
Therefore, the upper quartile, Q3, of the given data set is 54.
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F=ma find out f if m-26 and a-3 please help
Answer:
78
Step-by-step explanation:
26 + 26 + 26 = 78
What is the solution set for 6x - 5y > 30?
Graph the solution set of the linear inequality in the coordinate plane.
. First, select the Graph button to graph the line and choose the line style. To graph a line, select two points in the
coordinate plane. A line will connect the points.
. Then select the Solution Set button to select the desired region.
Graph
Line Type solid
Solution Set
2
1
2
hp
The (5, 0) is the x-intercept and Y-intercept is ( 0, 6 ).
How to calculated the x,y intercept?6x−5y=30
Find the x-intercepts.
Substitute 0 for y and solve for x to determine the x-intercept(s).
6x−5⋅0= 30
Solve the equation.
Tap for additional steps... x = 5 point-form x-intercepts.
( 5, 0 ) are the x-intercept(s)
Find the y-intercepts.
Substituting 0 for x and solving for y will yield the y-intercept(s).
6 ( 0 ) − 5 y = 30
Put the equation to rest.
Reduce the complexity of 6 ( 0 ) 5 y.
Add 0 to 6 to multiply.
0−5y= 30
Subtract 5 years from 0
−5y= 30
Simplify by multiplying each term in y = 5 by 5 before dividing again.
Each term in 5 y = 30 should be divided by 5.
−5y/−5 = 30/−5
Condense the left side.
Get rid of the common element of − 5.
y=30/−5
Condense the right side.
Subtract 5 from 30.
y= −6
In point form, the y-intercept(s).
Y-intercept(s): ( 0, 6 )
Identify the intersections.
(5, 0) is the x-intercept.
Y-intercept(s): ( 0, 6 ).
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Doug makes a parallelogram-shape sign for his shop.
What is the area of this parallelogram?
Round to the nearest hundredth.
A. 5.32 ft²
B. 8.96 ft²
C. 14.28 ft²
D. 17.02 ft²
PLS HELP!!!
Answer:
C, 14.28
Step-by-step explanation:
area = base * height
= (1.9+3.2) * 2.8
=14.28
Answer:
Answer is C! brainliest this time pls
Original function: F= 9/5C+32
Inverse function: C=F−32·5/9
Suppose we want to find the temperature in Celsius when it is 10 degrees Fahrenheit and when it is 90 degrees Fahrenheit. Which equation would you use? Why?
The inverse function is used to find the temperature in Celsius,
the temperature in celsius is -12.22°C and 32.22°C.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator).
Given expression for temperature calculation
Original function: F = 9/5C + 32
Inverse function: C = (F − 32)5/9
where C is temp. in Celsius and F is temp. in Fahrenheit,
so when the temperature is given in Fahrenheit we have to use the inverse function formula to calculate the temperature in degree celsius,
because it will be easy to calculate.
temperature = 10°F
C = (F − 32)5/9
C = (10 - 32)5/9
C = -22 x 5/9
C = -12.22°C
when temperature = 90°F
C = (90 - 32)5/9
C = 32.22°C
Hence the temperature is -12.22°C and 32.22°C.
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A health club has 2 employees who work on lead generation. Each employee contacts leads 20 hours a week and is paid $20 per hour: Each employee contacts an average of 200 leads a week. Approximately 8% of the leads become members and pay a onetime fee $100 Material costs are $190 per week, and overhead costs are $1,100 per week. a. Calculate the multifactor productivity for this operation in fees generated per dollar of input. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) b. The club's owner is considering whether to purchase a new software program that will allow each employees to contact 20 more leads per week. Material costs will increase by $260 per week. Overhead costs will remain the same. Calculate the new multifactor productivity if the owner purchases the software. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) c. How would purchasing the software affect productivity? (Enter the change in productivity as a percentage rounded to one decimal.)
The health club has 2 employees who work on lead generation. Each employee contacts leads for 20 hours a week and is paid $20 per hour. Approximately 8% of the leads become members and pay a one-time fee of $100. Material costs are $190 per week, and overhead costs are $1,100 per week. To analyze the productivity of the operation, we need to calculate the multifactor productivity in fees generated per dollar of input. The owner is also considering purchasing a new software program that would allow each employee to contact 20 more leads per week, but it would increase material costs by $260 per week. We need to calculate the new multifactor productivity if the software is purchased and determine how it would affect productivity.
a. To calculate the multifactor productivity, we need to determine the total fees generated and the total input costs. The total fees generated per week can be calculated as 8% of the total number of leads contacted multiplied by the one-time fee of $100, which is (0.08 * 200) * $100 = $1,600. The total input costs per week are the sum of employee wages, material costs, and overhead costs, which is (2 employees * 20 hours/week * $20/hour) + $190 + $1,100 = $2,490. Therefore, the multifactor productivity is $1,600 / $2,490 = 0.64.
b. If the owner purchases the software program and each employee can contact 20 more leads per week, the total number of leads contacted per week by both employees will be 2 * (200 + 20) = 440. The new material costs per week will be $190 + $260 = $450. The overhead costs remain the same at $1,100. The total input costs per week become (2 employees * 20 hours/week * $20/hour) + $450 + $1,100 = $1,650. The new multifactor productivity is $1,600 / $1,650 = 0.97.
c. The new multifactor productivity after purchasing the software program has increased to 0.97 from the previous value of 0.64. The change in productivity can be calculated as ((0.97 - 0.64) / 0.64) * 100 = 51.6%. Therefore, purchasing the software program would increase productivity by approximately 51.6%.
By analyzing the multifactor productivity and the impact of purchasing the software program, the owner can make an informed decision about whether the investment is worthwhile considering the potential increase in productivity.
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You roll a die with the sample space S=(1,2,3,4,5,6]. You define A as (1,2,4),B as [1,2,4,5,6],C as [5,6) and D as [2,3,6) Determine which of the following events are exhaustive and/or mutually exclusive
- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.
To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.
To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.
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