Therefοre, οnly the cοmparisοns (A and C) are true.
What is Cοmparisοn?In mathematics, a cοmparisοn is a statement that describes the relatiοnship between twο quantities οr expressiοns. Cοmparisοns can be used tο determine if twο values are equal, if οne value is greater than οr less than anοther value, οr if twο values are prοpοrtiοnal tο each οther.
A. 3.2 > 0.32
This cοmparisοn is true. 3.2 is greater than 0.32 because 3.2 has a whοle number value οf 3, which is greater than the whοle number value οf 0 in 0.32.
B. 4.7 < 4.70
This cοmparisοn is false. 4.7 is nοt less than 4.70 because the extra zerο in 4.70 dοes nοt change its value, and .7 is nοt less than .70.
C. 2.6 > 2.59
This cοmparisοn is true. 2.6 is greater than 2.59 because the extra 9 in 2.59 dοes nοt change its value, and 6 is greater than 5.
Therefοre, οnly the cοmparisοns (A and C) are true.
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which of the following is a point of tangency on the circle below
The correct option is C. Point B as only the line BC touching the circle at point B is tangent to the circle.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
We can observe that the line BC touches the circle at point B and the radius of the circle will be perpendicular to the line BC
Therefore, since the radius of the circle is perpendicular to the line BC at point B, then it is tangent to the circle
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The length of tile B is about 3.16228 inches. Which mark on the tape measure is closest to 3.16228 inches? Remember, the tape measure is marked in sixteenths of an inch.
The closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.
What is the mark on the tape?
To find the closest mark on the tape measure to 3.16228 inches, we need to convert 3.16228 inches to sixteenths of an inch, which is the unit used on the tape measure.
We can start by multiplying 3.16228 by 16 to convert it to sixteenths of an inch:
3.16228 * 16 = 50.59648
Next, we can round 50.59648 to the nearest whole number, which is 51. This means that the closest mark on the tape measure to 3.16228 inches is the mark for 51 sixteenths of an inch.
Note that we can also convert 3.16228 inches to eighths of an inch by multiplying by 8, which gives us:
3.16228 * 8 = 25.29824
Rounding 25.29824 to the nearest whole number gives us 25. This means that the closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.
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The residual plot shows the residuals for a person's age and their vertical jump (in inches). Which statement best
assesses the linearity of the relationship between age and vertical jump if it is known that the scatterplot appears to
be approximately linear?
Although it is given that the scatterplot is approximately linear, because the residual plot has no obvious pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is
not appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is not appropriate to use the line of best fit to predict vertical jump based on age.
The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:
Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.
The second option is correct.
What is a residual plot ?
A residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.
If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.
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Answer:
thx to the comments
Step-by-step explanation:
A triangular prism and its net are shown below. Please answer the questions EASY 20 points
Answer: SEND ME THE PIC
Step-by-step explanation:
Roberto bought a $400,000 house, paying 24% down, and financing the rest at 6.2% interest for 30 years. Her
monthly payments are $1861.91. How much will he really pay for her $400,000 house?
Roberto will pay a total of $
for the house.
Answer:
24% of $400,000 = 0.24 x $400,000 = $96,000
The amount he financed is:
$400,000 - $96,000 = $304,000
To calculate the total amount Roberto will pay for the house, we need to add up the principal (the amount he borrowed), the interest, and any fees or charges. We can use the formula for the monthly payment of a mortgage to find the total amount:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
where M is the monthly payment, P is the principal, i is the monthly interest rate (6.2% divided by 12), and n is the total number of payments (30 years times 12 months per year).
Plugging in the values, we get:
$1861.91 = $304,000 [ 0.00516667(1 + 0.00516667)^360 ] / [ (1 + 0.00516667)^360 - 1]
Solving for P, we get:
P = $304,000
So the total amount Roberto will pay for the house is:
$96,000 (down payment) + $1861.91 x 360 (monthly payments for 30 years) = $96,000 + $670,287.60 = $766,287.60
Therefore, Roberto will pay a total of $766,287.60 for the $400,000 house.
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more
than 2 times the number of marbles Mark has, how many does each boy have to sell if the total number
of marbles is 71?
Mark has 23 marbles and Don has 48 marbles.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Mark and Don, are selling their marbles at a garage sale. Don has more marbles than Mark and his number of marbles is equal to "2 more than 2 times the number of marbles Mark has."
Let x be the number of marbles that Mark has. Then, we can represent the number of marbles that Don has as 2x + 2.
Since the total number of marbles is 71, we can set up the equation:
x + (2x + 2) = 71
Simplifying the left side of the equation, we get:
3x + 2 = 71
Subtracting 2 from both sides, we get:
3x = 69
Dividing both sides by 3, we get:
x = 23
So Mark has 23 marbles. To find out how many marbles Don has, we can substitute x = 23 into the expression we derived earlier:
2x + 2 = 2(23) + 2 = 48
Therefore, Don has 48 marbles.
In total, they have 23 + 48 = 71 marbles, as given in the problem statement.
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Jerry wants to buy 4 Michelin tires from Sears, calculate his total price, tax rate is 8%.
Answer:
To calculate Jerry's total price, we need to know the cost of each Michelin tire from Sears. Let's assume that each tire costs $100.
The total cost of the 4 Michelin tires is:
4 tires x $100/tire = $400
Next, we need to calculate the amount of tax that Jerry will need to pay on his purchase. The tax rate is 8%, so we can calculate the amount of tax as:
$400 x 0.08 = $32
Finally, we can calculate Jerry's total cost by adding the cost of the tires to the tax:
$400 + $32 = $432
Therefore, Jerry's total price for 4 Michelin tires from Sears, including tax, is $432
The quotient of a number and negative eight is seven-eighths. Find the number.
The value of the numer is negative seven ( -7 ).
What is the unknown number?Given the statement in the question; the quotient of a number and negative eight is seven-eighths.
Let's translate the given statement into an algebraic equation to solve for the unknown number.
"The quotient of a number and negative eight" means that we are dividing the number by -8.
We can represent this using the division symbol " / ":
Let the number be represented by x.
x / (-8)
"Is" means "equals" " = "
"Seven-eighths" can be written as a fraction:
7/8
Nowm putting it all together, we get:
x / (-8) = 7/8
To solve for x, we can multiply both sides by -8:
x = (-8) × (7/8)
Simplifying the right side, we get:
x = -7
Therefore, the value of x is -7.
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What is the solution to 4^x = 5^x +^2
The solution to 4^x = 5^x +^2 is
x = -2log 5/( log 5 - log 4)
Option C is correct.
How do we calculate?We will rewrite the equation as:
4^x = 5^x * 5^2
applying the logarithm function to both sides of the equation.
log(4^x) = log(5^x * 5^2)
simplifying the right side of the equation, using the properties of logarithms,
log(4^x) = log(5^x) + log(5^2)
log(4^x) = xlog(4) = x2log(2)
log(5^x) + log(5^2) = xlog(5) + log(25)
Substituting these results back into the original equation, we have:
x2log(2) = x*log(5) + log(25)
x*(2*log(2) - log(5)) = log(25)
Divide both sides by (2*log(2) - log(5)), we get:
x = x = -2log 5/( log 5 - log 4)
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1. An airplane flies in the path shown by the vector CD on the graph below. What is the magnitude and direction of CD? (1 unit represents 1 mile)
The magnitude of CD is 5 miles and its direction is approximately 53.13°.
option D.
What is the magnitude and direction of the vector?To find the magnitude and direction of CD, we first need to calculate the distance between points C and D, which will give us the magnitude of the vector CD.
The distance formula between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values for points C and D, we get:
d = √((0 - (-4))² + (1 - 4)²)
= √(16 + 9)
= √(25)
= 5 miles
To find the direction of CD, we can use the arctan function to find the angle that CD makes with the x-axis.
tan(θ) = (y2 - y1) / (x2 - x1)
Plugging in the values for points C and D, we get:
tan(θ) = (1 - 4) / (0 - (-4))
= -3/4
Taking the arctan of both sides, we get:
θ = arctan(-3/4)
≈ -36.87°
However, since CD points in the negative x-direction, we need to add 90 degrees to get the correct direction.
θ = arctan(-3/4) + 90°
≈ 53.13°
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A secretary listed the frequency of calls by a patient to a doctor's office during a year, and the data is displayed in the histogram.
A histogram titled Calls To A Doctor. The x-axis is labeled Number of Calls and has intervals listed for 1 to 25, 26 to 50, 51 to 75, and 76 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every five units up to 60. There is a shaded bar for 1 to 25 that stops at 58, for 26 to 50 that stops at 34, for 51 to 75 that stops at 17, and for 76 to 100 that stops at 12.
Which of the following best describes the spread and distribution of the data?
The data is skewed to the higher values because many patients call the doctor several times a day when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The data is bimodal with a narrow spread because many patients call the doctor several times a day when they are sick.
The data is normal and has a wide spread because many patients only call the doctor once or twice a year when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
Define the terms spread and distribution?Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.
Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.
Based on the histogram description, the best answer is:
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.
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Answer:its b
Step-by-step explanation:
can you please solve this its urgent
Step-by-step explanation:
Think we can get a better picture, maybe more light? I wouldn't mind helping if you can
Find the values of a and b. Write your answers in simplest form.
The answer of the given question based on finding the values of a and b are 12 and 9, respectively.
What are Triangle?A triangle is geometric shape that consists of the three straight sides and three angles. Triangles are one of basic shapes in geometry and often used in the various mathematical applications.
Since triangles are similar, their corresponding sides are in the proportion. That is:
AB/DE = BC/EF = AC/DF
We can use this proportion to find the values of a and b.
From the diagram, we can see that:
AB = 12 + a
BC = 9 + b
AC = 15
DE = 8
EF = 6
Using the proportion, we get:
AB/DE = BC/EF
(12 + a)/8 = (9 + b)/6
Cross-multiplying, we get:
6(12 + a) = 8(9 + b)
72 + 6a = 72 + 8b
6a = 8b
a/b = 4/3
Similarly, using the other part of the proportion, we get:
AC/DF = 15/DF = (AB + BC)/(DE + EF) = (12 + a + 9 + b)/(8 + 6)
15DF = 21 + a + b
Substituting the value of a/b = 4/3, we get:
15DF = 21 + (4/3)b + b
15DF = 21 + (7/3)b
45DF = 63 + 7b
45DF = 7(b + 9)
Dividing both sides by 7, we get:
DF = (b + 9)
Substituting this value in the previous equation, we get:
45(b + 9) = 63 + 7b
45b + 405 = 63 + 7b
38b = 342
b = 9
Substituting the value of b in the equation a/b = 4/3, we get:
a/9 = 4/3
a = 12
Therefore, the values of a and b are 12 and 9, respectively.
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Which of the following is the same as 8(9+2) ?
8*9+8
8*9+2
8*9+8*2
9(8+2)
2(8+9)
According the question 89+82 expressiοn is the same as 8(9+2).
What is expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.
Algebraic expressiοns are classified οn the basis οf the number οf terms in the expressiοn. The variοus types οf algebraic expressiοns are:
Mοnοmial expressiοnsBinοmial expressiοnsTrinοmial expressiοnsPοlynοmial expressiοnsThe difference between expressiοns and equatiοns is that an expressiοn signifies a cοmbinatiοn οf numbers, variables, and οperatiοn symbοls whereas an equatiοn will always use an equal (=) οperatοr between twο math expressiοns.
The expressiοn 8(9+2) can be simplified using the distributive prοperty οf multiplicatiοn οver additiοn:
8(9+2) = 89 + 82
Therefοre, the answer is: 89+82
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Find the linear function with the following properties.
f(0)=6
Slope of f=−9
Answer: y=-9x+6
Step-by-step explanation: The common form of a line is the Slope-Intercept form which is y=Mx+B. M represents the slope of the line, B represents the y-intercept, and x and y represent a point on the xy plane such as (1,2). The y-intercept is the point at which x = 0. The slope of a line is given by the equation (y2-y1)/(x2-x1) where (y1,x1) and (y2,x2) are points on a coordinate plane.
In this problem, we are already given M or the slope which is -9. We are also given the y-intercept but it's not as clear. f(x)=y represents a general function where you input an x-coordinate x into f(x) and the function produces a y-coordinate y. If we had a function f(x)=2x+1 and we input 3 as x we replace all the x's with 3 which gives us f(x)=2(3)+1=7. f(3)=7 which can be written as (3,7) being a point on the function. Lines in the coordinate plane represent linear functions because they have a constant slope due to no exponents.
Here, we are told f(0)=6 which can be rewritten as (0,6) being a point on the linear function. I said earlier that the y-intercept is when x=0 and this point has x=0. y=6 when x=0 so 6 is our y-intercept. Now we plug into the slope-intercept form y=mx+b giving us y=-9x+6 which is our answer.
Hope this helps! For practice, find the linear function that has the two points (1,2) and (3,6) on it.
What is the perimeter of the rectangle in the coordinate plane?
_______________________________
(reporting spams/wrong answers)
(giving brainliest to the correct answer)
_______________________________
Answer:
40 units
Step-by-step explanation:
12+12+8+8=40 units
Bridge B is 186 feet shorter than Bridge A. The combined length of the two bridges is 9456 feet. Find the length of each bridge.
Answer:
Length of Bridge A = 4821
Length of Bridge B = 4635
Step-by-step explanation:
Let's call the length of Bridge A "x" which is measured in feet. According to the problem, the length of Bridge B is "186 feet shorter than Bridge A." This can be written as the following:
Length of Bridge B = x - 186
The problem also tells us that the "combined length of the two bridges is 9456 feet," which we can write as:
Length of Bridge A + Length of Bridge B = 9456
Now we can substitute the expression we found for the length of Bridge B into this equation. This can be shown as the following:
x + (x - 186) = 9456
Simplifying this equation, we can combine the two x terms and get the following:
2x - 186 = 9456
Now, we can solve for x
2x - 186 + 186 = 9456 + 186
2x = 9642
x = 4821
So the length of Bridge A is 4821 feet. To find the length of Bridge B, we can use the expression we found earlier:
Length of Bridge B = x - 186 = 4821 - 186 = 4635
Therefore, the length of Bridge A is 4821 feet, and the length of Bridge B is 4635 feet.
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When calculating simple interest, what must you do if you want to invest for months instead of years?
The circle below has center o, and its radius is 4 yd. Given that m
Answer:
length = 0.89π yd
area = 14.22π yd^2
Step-by-step explanation:
Given r = 4, θ = 40
Length of an arc = 2πr(θ/360º)
l = 2π(4)(40/360) = π(320/360) = π(8/9) = 0.89π
Given r = 4, θ = 360 - 40 = 320
Area of a sector of circle = πr^2(θ/360º)
A = π(4^2)(320/360) = π(16)(8/9) = 14.22π
From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread. Which expression tells the weight of the flour left in the bag?
2-0.25
2-1.4
2-0.14
2-0.025
2.5-2
The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25
What is an expressiοn?A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.
Here, we have
Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.
We have to find the expression that tells the weight of the flour left in the bag.
Marcella took 1/4 pound to bake bread = 0.25
If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.
Hence, the expression that tells the weight of the flour left in the bag is 2 - 0.25
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Find the two linearly independent solutions of the LODE following for x>0, and determine at least the first four leading terms in the second solution y(2). 9x²y" - 6xy' + 2y = 0
Please, I need the solution
Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
What is the solution to the equationThe given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:
9r^2 - 6r + 2 = 0
Using the quadratic formula, we find the roots to be:
r = (1/3) ± i/sqrt(3)
Thus, the general solution to the differential equation is:
y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))
To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:
y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))
To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:
y2(x) = v(x) * y1(x)
Substituting this into the differential equation, we obtain:
9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0
Simplifying this equation by dividing by x^2*y1(x), we get:
9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0
where r = sqrt(3)
This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:
v(x) = x^m
Substituting this into the equation, we obtain:
9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0
Simplifying this equation, we get:
9m^2 + 6m + 1 = 0
Using the quadratic formula, we find the roots to be:
m = (-1/3) or (-1/3)
Thus, the second solution is given by:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)
To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:
ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...
Substituting this into the second solution, we obtain:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]
Simplifying this expression, we get:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...
Thus, the first four leading terms in the second solution are:
y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
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The Good’n’Fresh Grocery Store has two checkout lanes and four employees. Employees are equally skilled, and all are able to either operate a register (checkers) or bag groceries (baggers). The store owner assigns one checker and one bagger to each lane. A lane with a checker and a bagger can check out 46 customers per hour. A lane with a checker only can check out 25 customers per hour.
a. In terms of customers checked out per hour, what are total output and average labor productivity for the Good’n’Fresh Grocery Store?
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
Total output:
92
customers per hour.
Average productivity:
24
customers per hour, per worker
b. The owner adds a third checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 1
Two lanes with only checkers and one lane with a checker and a bagger.
Two lanes with a checker and bagger and one lane left empty.
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
What are total output and average labor productivity (in terms of customers checked out per hour) now?
Total output:
customers per hour
Average productivity:
customers per hour, per worker
c. The owner adds a fourth checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 2
Four lanes with checkers only.
Do not use the fourth lane.
Two lanes with one checker and one bagger each.
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
Total output:
customers per hour
Average productivity:
customers per hour
The owner adds a fifth checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 3
Two lanes with only checkers and one lane with a checker and a bagger.
Do not use the fifth lane.
Two lanes with one checker and one bagger at each.
Do you observe diminishing returns to capital in this example?.
multiple choice 4
Yes, adding a third lane will not increase output
Yes, adding a fifth lane will not increase output.
Yes, adding a fourth lane will not increase output
No, adding all five lanes will increase output.
41 clients can be checked out in an hour on a lane with a checker and a bagger. Only 25 people can be checked out per hour at a checker-only line.
a. The Good'n'Fresh Grocery Store's total production and average labor productivity are 92 customers per hour and 23.5 customers per hour per worker, respectively.
b. Two lanes with a checker and a bagger, and one lane with a checker only, are the ideal configurations for reassigning the workers to duties.
a. The total output of the Good’n’Fresh Grocery Store is:
Total output = 2 lanes x 46 customers/lane/hour + 2 lanes x 25 customers/lane/hour
= 92 customers/hour
The average labor productivity is:
Average productivity = Total output / Total number of workers
= 92 customers/hour / 4 workers
= 23 customers/hour/worker
≈ 23.0 customers/hour/worker
Therefore, the total output is 92 customers per hour, and the average labor productivity is 23.0 customers per hour, per worker.
b. With three lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and one lane with a checker only.
This way, each lane will have one checker and one bagger, which is the most efficient way to operate a lane. The total output will be:
Total output = 3 lanes x 46 customers/lane/hour
= 138 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 138 customers/hour / 4 workers
= 34.5 customers/hour/worker
≈ 34.5 customers/hour/worker
Therefore, the total output is 138 customers per hour, and the average labour productivity is 34.5 customers per hour, per worker.
c. With four lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and two lanes with a checker only.
This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:
Total output = 4 lanes x 46 customers/lane/hour
= 184 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 184 customers/hour / 4 workers
= 46 customers/hour/worker
≈ 46.0 customers/hour/worker
Therefore, the total output is 184 customers per hour, and the average labour productivity is 46.0 customers per hour, per worker.
d. With five lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and three lanes with a checker only.
This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:
Total output = 5 lanes x 46 customers/lane/hour
= 230 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 230 customers/hour / 4 workers
= 57.5 customers/hour/worker
≈ 57.5 customers/hour/worker
Therefore, the total output is 230 customers per hour, and the average labour productivity is 57.5 customers per hour, per worker.
e. Yes, we observe diminishing returns to capital in this example because adding more lanes does not increase output proportionally. Adding a third lane increases output by 46 customers/hour, adding a fourth lane increases output by 46 customers/hour, and adding a fifth lane increases output by 46 customers/hour. Therefore, the marginal output of adding each additional lane is decreasing. The correct multiple-choice answer is:
Certainly, adding a fifth lane won't boost productivity.
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A family drives 509 miles to their vacation destination. It takes them 8.6 hours to get there. What was their average velocity in miles per hour?
Answer:
Their average velocity during their trip was 59.19 miles per hour.
Step-by-step explanation:
To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:
Average velocity = total distance ÷ time
In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:
Average velocity = 509 miles ÷ 8.6 hours
Simplifying this equation, we get:
Average velocity = 59.19 miles per hour (rounded to two decimal places)
Therefore, the family's average velocity during their trip was 59.19 miles per hour.
5x-4y=3(x+3) slope and y+x intercept
Answer:
Step-by-step explanation:
To find the slope of the line represented by the equation 5x-4y=3(x+3), we can rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
5x - 4y = 3(x + 3)
5x - 4y = 3x + 9
5x - 3x = 4y + 9
2x = 4y + 9
y = (2/4)x - 9/4
So, the slope of the line is 2/4, which can be simplified to 1/2.
To find the y-intercept, we can set x = 0 in the equation:
y = (1/2)(0) - 9/4
y = -9/4
Therefore, the y-intercept is -9/4.
To find the x-intercept, we can set y = 0 in the equation:
0 = (1/2)x - 9/4
9/4 = (1/2)x
x = (9/4) / (1/2)
x = 9/2
Therefore, the x-intercept is 9/2.
Answer:
Slope: -1/2 Y-Intercept: -9/4
Step-by-step explanation:
5x - 4y = 3x + 9
Subtract 3x from both sides
2x - 4y = 9
Divide both sides by -4
y = (-1/2)x + (-9/4)
Answer this question please
The transformation that it could have been is either a rotation or a reflection, over one of the vertices of the figure.
What are transformations on a figure?The possible transformations on a figure are listed as follows:
Translation: Translation left/right or down/up, moving all vertices.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, hence all vertices are changed.Either a reflection or a rotation can happen over one of the vertices of the graph, which will keep it's coordinates constant, and thus the transformation in the context of this problem is either one of these two.
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A cuboid has faces with areas 24, 32, and 48 square centimeters. what are the lengths of its sides?
Answer:
Let's denote the length, width, and
height of the cuboid as "l", "w", and
"h, respectively. Then, we have:
lw= 24 (Area of one face)
Ih 32 (Area of another face)
wh 48 (Area of the third face)
To solve for the dimensions of the
cuboid, we can use a system of
equations. We can start by solving
for one of the variables in terms of
the other two. For example, from the
first equation, we have:
W 24/
Substituting this into the second
equation, we get:
Ih 32
I(24/)h = 32
24h 32
h 32/24
h 4/3
Next, we can substitute the values of
h and w into the third equation to
solve for:
wh = 48
I(24/)(4/3) = 48
I2 72
= sqrt(72)
I= 6sqrt(2)
Finally, we can use the values of I
and w to solve for the remaining
dimension:
lw 24
(6sqrt(2))(24/(6sqrt(2))) = 24
W = 4sqrt(2)
Therefore, the lengths of the sides of
the cuboid are:
Length () = 6v2 cm
Width (w) = 4/2 cm
Height (h) = 4/3 cm
A circle has a circumference of 20 ft. What is the
radius of the circle?
Step-by-step explanation:
The formula to calculate the circumference of a circle is:
Circumference = 2πr
where "r" is the radius of the circle and "π" is the mathematical constant pi, approximately equal to 3.14159.
Given that the circumference of the circle is 20 ft, we can plug in the values into the formula and solve for "r":
20 = 2πr
Divide both sides of the equation by 2π:
r = 20 / (2π)
Simplify the expression by using the approximation of π as 3.14159:
r = 20 / (2 x 3.14159)
r = 3.1831 ft (rounded to four decimal places)
Therefore, the radius of the circle is approximately 3.1831 feet.
The city of Pineville held a talent contest. Judges rated the contestants on a scale from 1 to
10. A singer was rated 7.4, while a juggler was rated 7.0. The median rating was 7.9, and the
interquartile range was 0.8. The winner was a magician who was rated 9.7.
Which number best describes a typical rating in the contest?
0.8
7.4
7.9
9.7
The answer of the given question based on the number best describes a typical rating in the contest the answer is 7.9.
What is Median?The median is measure of central tendency in statistics that represents middle value of dataset. It is value that separates highest 50% of values from the lowest 50%.
To find median of a dataset, you first need to sort data in ascending or descending order.
The median rating is 7.9, which means that half of the contestants scored above 7.9 and half scored below. This suggests that 7.9 is a representative value of the ratings overall.
Additionally, the interquartile range (IQR) is a measure of the spread of the middle 50% of the ratings, and it is given as 0.8. This means that the ratings between the 25th and 75th percentile fall within a range of 0.8, which suggests that the ratings are fairly tightly clustered around the median of 7.9.
Therefore, the number that best describes a typical rating in the contest is 7.9.
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A high school drama club is selling tickets for the spring production. One day the president sold 12 adult tickets and 5 child tickets for a total of $169. The next day the president sold 22 adult tickets and 10 child tickets for a total of $314. Let a represent the cost of one adult ticket. Let c represent the cost of one child ticket. Which system of equations will solve for a and c?
12 a + 5 c = 314. 22 a + 10 c = 169.
12 a + 5 c = 169. 22 a + 10 c = 314.
5 a + 12 c = 314. 22 a + 10 c = 169.
22 a + 5 c = 169. 12 a + 10 c = 314.
Mark this and return
The cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
What is system οf equatiοn?A system οf linear equatiοns can be sοlved graphically, by substitutiοn, by eliminatiοn, and by the use οf matrices.
The cοrrect system οf equatiοns tο sοlve fοr a and c is:
12a + 5c = 169 (equatiοn 1)
22a + 10c = 314 (equatiοn 2)
These equatiοns represent the tοtal ticket sales and revenue οn twο different days.
Tο sοlve this system, we can use the methοd οf eliminatiοn.
-24a - 10c = -338
22a + 10c = 314
-2a = -24
Dividing bοth sides by -2:
a = 12
Nοw we can substitute a = 12 intο equatiοn 1 tο sοlve fοr c:
12(12) + 5c = 169
144 + 5c = 169
5c = 25
c = 5
Therefοre, the cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
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0 is greater than or equal to 0
A.) No solution
B.) all real numbers
The answer of the given question based on the inequality is option B) all real numbers.
What are Real numbers?A real numbers are set of numbers that include all rational and irrational numbers, which can be expressed as decimal expansions that go on forever without repeating. The set of real numbers is denoted by symbol ℝ and includes numbers such as 1, 2, 3, -4, -5/6, π, √2, and e.
B.) all real numbers
A statement "0 is greater than or equal to 0" is always true, regardless of value of variable or any other conditions. This is because any number is always equal to the itself, and 0 is no exception. Therefore, solution to this inequality is all the real numbers.
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