It had started at (0,120) and ran for 40 minutes, Coordinates would be approximately (60.00, 103.92).
a) To find the coordinates after 20 minutes of running counter-clockwise starting at (120,0), we need to determine the distance covered in that time period.
Since you are running at a speed of 3 meters per second, in 20 minutes (or 20 * 60 = 1200 seconds), you would have covered a distance of 3 * 1200 = 3600 meters.
Given that the equation of the circular track is x^2 + y^2 = 14400, which represents a circle with a radius of 120 units (since the radius squared is 14400), we can determine your new position on the track.
Starting from (120,0) and moving counter-clockwise, you would have traveled a distance of 3600 meters along the circumference of the circle. This corresponds to a fraction of 3600 / (2 * π * 120) = 15 / π of the circle's circumference.
Using this fraction, we can calculate the angle in radians by multiplying it by 2π. Therefore, the angle is 2π * (15 / π) = 30 radians.
To find the new coordinates, we can use the polar coordinates formula:
x = r * cos(θ)
y = r * sin(θ)
Plugging in the values:
x = 120 * cos(30) ≈ 103.92
y = 120 * sin(30) ≈ 60.00
So, after 20 minutes of running counter-clockwise, your coordinates would be approximately (103.92, 60.00).
b) If you had started at (0,120) and ran for 40 minutes, the process is similar. Since you are running at a speed of 3 meters per second, in 40 minutes (or 40 * 60 = 2400 seconds), you would have covered a distance of 3 * 2400 = 7200 meters.
Using the same circle equation x^2 + y^2 = 14400, we determine the new position on the track.
Starting from (0,120) and moving counter-clockwise, you would have traveled a distance of 7200 meters along the circumference of the circle. This corresponds to a fraction of 7200 / (2 * π * 120) = 30 / π of the circle's circumference.
The angle in radians is given by 2π * (30 / π) = 60 radians.
Using the polar coordinates formula:
x = r * cos(θ)
y = r * sin(θ)
Plugging in the values:
x = 120 * cos(60) ≈ 60.00
y = 120 * sin(60) ≈ 103.92
So, if you had started at (0,120) and ran for 40 minutes, your coordinates would be approximately (60.00, 103.92).
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Find the amount of the payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period.
$65000 money earns 6% compounded semiannually for
2 1/2 years
Total cost (in rands) = R300 + (Number of minutes - 500) * R0.50
How to find the amount of the payment to be made into a sinking fundTo calculate the total cost (in rands) for Call Package 2, we can use the following formula:
Total cost (in rands) = Monthly rental + (Number of minutes - Free minutes) * Cost per minute
Let's break down the formula:
Monthly rental: This is a fixed cost that MaNdlovu pays every month for the call package. In this case, the monthly rental for Package 2 is R300.
Number of minutes: This refers to the total number of minutes MaNdlovu uses for her calls.
Free minutes: The first 500 minutes are free, meaning MaNdlovu does not have to pay for them.
Cost per minute: This is the cost per minute for the calls that are not covered by the free minutes. In this case, the cost per minute is R0.50.
By substituting the values into the formula, we get:
Total cost (in rands) = R300 + (Number of minutes - 500) * R0.50
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an inventor is designing a machine that will have two gears. the first gear will complete one revolution every 8x squared y seconds. the second gear will complete one revolution every 6x to the third power y squared seconds. how often will both of the gears be in their starting positions at the same time
Answer:
every 24x^3y^2 seconds
Step-by-step explanation:
To determine how often both gears will be in their starting positions at the same time, we need to find a common multiple of the two revolution times.
The first gear completes one revolution every 8x^2y seconds, and the second gear completes one revolution every 6x^3y^2 seconds.
To find a common multiple, we need to factorize the revolution times:
8x^2y = (2^3)(x^2)(y)
6x^3y^2 = (2)(3)(x^3)(y^2)
The common multiple should include all the prime factors with their highest powers. Therefore, the common multiple would be:
(2^3)(3)(x^3)(y^2) = 24x^3y^2 seconds.
So, both gears will be in their starting positions at the same time every 24x^3y^2 seconds.
Calculate the total cost of an item bought at a negotiated price of $21,980 with 7.6 percent sales tax and a $82 registration fee.
$22,473.18
$22,962
$23,656.71
$23,732.48
The total cost of the item 23, 732.48 dollars.
How to find the total cost of the item?The item was negotiated at a price of $21,980 with 7.6 percent sales tax
and a $82 registration fee.
Therefore, let's find the total cost of the item.
Hence,
The sales tax is a consumption tax on the sale of goods and services. Therefore,
sales tax = 7.6 % of 21980
sales tax = 7.6 / 100 × 21980
sales tax = 167048 / 100
sales tax = 1670.48 dollars
Therefore,
total cost of items = 21980 + 1670.48 + 82
total cost of items = 23, 732.48 dollars
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If a whole number is divided by another non-zero whole number, then the remainder is always smaller than
Answer:
The remainder is always smaller than the divisor.
For example, if we divide 12 by 5, we get 2 with a remainder of 2. The remainder is 2, which is smaller than the divisor, which is 5.
This is because the remainder is the part of the dividend that is not divisible by the divisor. In this case, 12 is not divisible by 5, so the remainder is 2.
The remainder can also be zero if the dividend is divisible by the divisor. For example, if we divide 10 by 5, we get 2 with a remainder of 0. This is because 10 is divisible by 5, so the remainder is 0.
In general, the remainder is always smaller than the divisor.
The volume of a cylinder is 368 cubic inches and the radius of the cylinder is 4 inches. What is the height of the cylinder?
Answer: the answer is h=7.32in
A research company desires to know the mean consumption of milk per week among males over age 40. They believe that the milk consumption has a mean of 3 liters, and want to construct a 85% confidence interval with a maximum error of 0.07 liters. Assuming a standard deviation of 1.3 liters, what is the minimum number of males over age 40 they must include in their sample? Round your answer up to the next integer.
The minimum number of males over age 40 that the research company must include in their sample is 715.
To determine the minimum number of males over age 40 needed in the sample, we can use the formula for the sample size in a confidence interval:
n = (Z * σ / E)^2
Where:
n = sample size
Z = z-score corresponding to the desired confidence level (85% confidence interval corresponds to a z-score of approximately 1.44)
σ = standard deviation of the population
E = maximum error or margin of error
Given:
Z = 1.44
σ = 1.3 liters
E = 0.07 liters
Substituting these values into the formula, we have:
n = (1.44 * 1.3 / 0.07)^2
n = (1.872 / 0.07)^2
n = 26.742857^2
n ≈ 714.285714
Since we cannot have a fraction of a person in the sample, we need to round up the sample size to the next integer:
n = ceil(714.285714) = 715
Therefore, the minimum number of males over age 40 that the research company must include in their sample is 715.
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sin¹(x)-cos¹ (x)/sin²(x)-cos² (x) =1
An isosceles triangle has equal sides where PQ = PR and base angles of 65⁰. QX = XR = 2.64 cm. Find a) PQ b) PX
Answer:
In an isosceles triangle, the sides opposite the equal angles are equal in length. Let's solve the given problem using the given information.
a) To find PQ, we need to find the length of the equal sides. Since QX = XR = 2.64 cm, we know that PQ = PR. Therefore, PQ = PR = 2.64 cm.
b) To find PX, we can use the concept of the Law of Cosines. In an isosceles triangle, the base angles are equal, so the angle at P is 65°, and the opposite side is PX.
Using the Law of Cosines formula:
c² = a² + b² - 2ab * cos(C)
Where c is the side opposite angle C, and a and b are the other two sides.
In our case, we have:
a = PQ = 2.64 cm
b = PR = 2.64 cm
C = 65°
We want to find PX, so c = PX.
Substituting the values into the formula:
PX² = (2.64)² + (2.64)² - 2(2.64)(2.64) * cos(65°)
PX² ≈ 6.9696 + 6.9696 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262
PX² ≈ 13.9392 - 11.1197
PX² ≈ 2.8195
Taking the square root of both sides, we get:
PX ≈ √2.8195
PX ≈ 1.678 cm
Therefore, a) PQ = PR = 2.64 cm, and b) PX ≈ 1.678 cm.
Step-by-step explanation:
If triangle RST is congruent to triangle WXY, by the Angle-Side-Angle Theorem, which transformation would not map triangle RST to triangle WXY?
a. Horizontal shift 4 units left
b. Reflection across the y axis
C. Dilation with a scale factor of 3
d. Rotation of 90° around the origin
Answer:
C. dilation with a scale factor of 3
Step-by-step explanation:
If triangle RST is congruent to triangle WXY by the Angle-Side-Angle Theorem, then a **dilation with a scale factor of 3** would not map triangle RST to triangle WXY. Congruent triangles have the same shape and size, meaning that their corresponding sides and angles are equal. A dilation changes the size of a figure but not its shape, so it would not preserve congruence between the two triangles.
evaluate 8x-4y when x=2 and y=3 (a)4 (b)28 (c)22 (d)18
Answer:
(a) 4
Step-by-step explanation:
Let's start with the equation:
8x-4y
Since we already have the values of x and y, we can solve out equation.
8(2)-4(3)
16-12=4
The answer is (a)4
pls help, due today !
(a) the function which has the graph with greatest slope is function 3.
(b) The function which has the graph with a y intercept closest to 0 is function 2.
(c) The functions which have graphs with y intercepts greater than 4 is function 4.
Given are 4 functions.
For function 1, consider two points (1, -3) and (0, -4).
Slope = (-4 - -3) / (0 - 1) = 1
For function 2, consider two points (1, -6) and (0, -1).
Slope = (-1 - -6) / (0 - 1) = -5
For function 3,
Slope = 4
For function 4,
Slope = -3
Greatest slope is for function 3.
y intercept is the point where the graph touches the Y axis. x coordinate will be 0 at that point.
For function 1,
y intercept = -4
For function 2,
y intercept = -1
For function 3,
y intercept = 3
For function 4,
y intercept = 5
The graph which has y intercept closest to 0 is function 2.
The functions which have graphs with y intercepts greater than 4 is function 4.
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16. What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft
Answers 96 ft³3 76 ft³ 152 ft³ 192 ft³
The volume of the composite figure is 228 ft³.
To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.
From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.
First prism:
Length = 8 ft, Width = 4 ft, Height = 6 ft
Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³
Second prism:
Length = 3 ft, Width = 2 ft, Height = 6 ft
Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³
Now, let's add the volumes of both prisms:
192 ft³ + 36 ft³ = 228 ft³
Therefore, the volume of the composite figure is 228 ft³.
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What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft
Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³
Jennifer and Elena are also selling tickets to the
dance. Jennifer starts with 50 tickets to sell and sells
2 tickets per day. Elena starts with 70 tickets to sell
and sells 4 tickets per day. If Jennifer and Elena start
selling tickets on the same day, on what day will they
have the same number of tickets left to sell?
On the 10th day, Jennifer and Elena will have the same number of tickets left to sell.
We have,
To determine the day when Jennifer and Elena will have the same number of tickets left to sell, we can set up an equation to represent the situation.
Let's assume x represents the number of days that have passed since they started selling tickets.
For Jennifer, the number of tickets she has left to sell after x days can be represented as:
Tickets left for Jennifer = 50 - 2x
For Elena, the number of tickets she has left to sell after x days can be represented as:
Tickets left for Elena = 70 - 4x
To find the day when they have the same number of tickets left to sell, we set the two equations equal to each other and solve for x:
50 - 2x = 70 - 4x
Simplifying the equation:
2x - 4x = 70 - 50
-2x = 20
x = -10
Since we can't have a negative number of days, it means that they will have the same number of tickets left to sell after 10 days.
Therefore,
On the 10th day, Jennifer and Elena will have the same number of tickets left to sell.
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Help me solve this please
Answer:
622m²
Step-by-step explanation:
a right rectangular prism will have 6 sides and the parallel sides of the prism will be the same size
so we work out the given surface areas and multiply each by 2
7 x 11 = 77
times 2 is 154
11 x 13 = 143
times 2 is 286
7 x 13 = 91
times 2 is 182
then we add it all up
154 + 286 + 182 = 622m²
Use diagram below to answer the following question.
The circumference of the circle is 18.84.
We have,
Radius = 3
Now,
The circumference of a circle.
= 2πr
Substituting r and π = 3.14.
= 2 x 3.14 x 3
= 18.84
Thus,
The circumference of the circle is 18.84.
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One month Sam rented 3 movies and 5 video games for a total of $32. The next month, he rented 12 movies and 2 video games for a total of $29. Find the rental cost for a movie and a video game.
Using a system of equations, the rental cost for a movie and a video game is as follows:
Movie = $1.50Video game = $5.50.What is a system of equations?A system of equations is two or more equations solved concurrently or at the same time.
A system of equations is also described as simultaneous equations.
Movies Video Total
Games Cost
First month rental 3 5 $32
Second month rental 12 2 $29
Let the rental cost per movie = x
Let the rental cost per video game = y
Equations:
3x + 5y = 32 ... Equation 1
12x + 2y = 29 ... Equation 2
Multiply Equation 1 by 4:
12x + 20y = 128 ... Equation 3
Subtract Equation 2 from Equation 3:
12x + 20y = 128
-
12x + 2y = 29
18y = 99
y = 5.5
Substitute y = 5.5 in Equation 1 or 2:
12x + 2y = 29
12x + 2(5.5) = 29
12x + 11 = 29
12x = 18
x = 1.5
Thus, based on simultaneous equations, the rental cost for a movie is $1.50 while a video game's is $5.50.
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baez has hit 31.25 of the time he is at bat for the last 7 games. If he has 10 hits how many total does he have.
To answer the original question, if Baez has 10 hits in 32 at-bats, he would have a total of 10 hits.
To answer this question, we first need to figure out how many at-bats Baez has had over the last seven games.
Since he hits 31.25% of the time he is at bat, we can assume that he has had 100/31.25 = 3.2 at-bats per hit. Therefore, he has had 32 at-bats over the last seven games (10 hits x 3.2 at-bats per hit).
Now that we know Baez has had 32 at-bats, we can calculate his batting average by dividing the number of hits he has (10) by the number of at-bats (32). This gives us a batting average of 0.3125, or 31.25%.
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Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the given curve
about the y-axis.
y = 0.25 - (x-4)²
Answer:
4π/3 ≈ 4.18879 cubic units
Step-by-step explanation:
You want the volume of revolution formed by revolving the 1st-quadrant area under y = 0.25 -(x -4)² around the y-axis.
Volume
There are several ways to find the volume of revolution. One can integrate a differential of volume, where that differential is a cylindrical shell or a washer. Alternatively, one can multiply the area under the curve by the centerline length of the path of revolution. We choose this latter approach.
AreaThe area in the first quadrant of the region being rotated can be found as the integral between its x-intercepts.
The x-intercepts are found by ...
0 = 1/4 -(x -4)²
x -4 = ±√(1/4) = ±1/2
x = 4 ± 1/2 = {3.5, 4.5} . . . . . . x-intercepts
Then the area is ...
[tex]\displaystyle\int_{3.5}^{4.5}(0.25-(x-4)^2)\,dx=\left[0.25x-\dfrac{1}{3}(x-4)^3\right]_{3.5}^{4.5}\\\\\\=0.25(1)-\dfrac{1}{3}(0.5^3-(-0.5)^3)=\dfrac{1}{6}\qquad\text{square units}[/tex]
RevolvedThe radius from the y-axis to the line of symmetry of the area is 4 units, so the length of the rotation path is
C = 2πr = 2π(4) = 8π
The product of this path length and the area is ...
V = C·A = (8π)(1/6) = 4π/3
The volume of the solid is 4π/3 cubic units.
__
Additional comment
The area under a symmetrical portion of a parabola is 2/3 of the area of the enclosing rectangle. The portion of the parabola in the 1st quadrant is 1 unit wide and 0.25 units high, so its area is (1)(1/4)(2/3) = 1/6 square unit, as we found above.
The second attachment shows the volume found using the cylindrical shell method.
<95141404393>
Find the area between the curves y=e^-0.3x and y=2.2x+1 from x=0 to x=2
From x = 0 to x = 2, the area of the region between the curves [tex]y = e^{-0.3x[/tex] and y = 2.2x + 1 is roughly 2.496 square units.
To determine the area, the intersection points of two curves must be identified, and the difference between the curves must be integrated over the provided time interval.
Finding the points of intersection by setting the two equations equal to each other:
[tex]e^{-0.3x[/tex] = 2.2x + 1
After graphing the two equations, we find that they intersect at approximately (0.380, 1.836) and (1.847, 5.080).
We can now find the area by integrating the difference between the curves across the given range [0, 2].
To get the area between two curves, use the following formula:
Area = ∫(upper curve - lower curve) dx
Area = ∫(2.2x + 1 - [tex]e^{-0.3x[/tex] ) dx
Solving,
Area ≈ 2.496
Hence the area between the curves y = [tex]e^{-0.3x[/tex] and y = 2.2x + 1 from x = 0 to x = 2 is approximately 2.496 square units.
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list price: $6.40 dicount rate :15%. find the discount and find the sale price Emergency
The sale price is $5.44 while the discount is $0.96
What is an equation?An equation is an expression that is used to show how numbers and variables are related using mathematical operators
The list price of a goods is $6.40 and the discount rate is 15%, hence:
Discount = 15% of list price = 0.15 * $6.40 = $0.96
Sale price = List price - Discount = $6.40 - $0.96 = $5.44
The sale price is $5.44
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The surface area is ___
square feet.
The Surface Area of Prism is 17.6 ft².
We have,
Sides of triangle = 2 ft, 1 ft and 2.2 ft.
and, l = 3 ft, b = 1 ft and h= 2 ft
So, Surface Area of Prism
= (2 + 1 + 2.2)3 + 2 x 1
= 5.2 x 3 + 2
= 17.6 ft²
Thus, Surface Area of Prism is 17.6 ft².
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what is the range of f(x)?
Answer: 0,1
Step-by-step explanation:
Evaluate the expression.
15-2√ 3² + 16
=
Answer: 25
Step-by-step explanation:
bc
What is the sum of the first 43 terms of the sequence?
−282,−277,−272,−267,...
The sum of the first 43 terms of the sequence given below is -7611.
What is the arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
The formula for it is:
[tex]\text{a}_\text{n}=\text{a}+\text{D}(\text{n}-1)[/tex]
Given Sequence:
[tex]\sf -282,-277,-272,-267, \ ...[/tex]It represent an A.P. with
first term [tex]\sf a=-282[/tex]common difference [tex]\sf d =5[/tex]So, sum of 43 terms.
[tex]\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[2\times(-282)+(43-1)5][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[-564+210][/tex]
[tex]\text{S}_{43}=\frac{43}{2}\times[-354][/tex]
[tex]\text{S}_{43}={43}\times[-177][/tex]
[tex]\text{S}_{43}=\bold{-7611}[/tex]
Hence, the sum of the first 43 terms of the sequence given below is
-7611.
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Evaluate (4+1i)-(-6+4i)
The expression represents the subtraction of two Complex numbers, resulting in a new complex number with a real part of 10 and an imaginary part of -3i.
The expression (4 + 1i) - (-6 + 4i),the subtraction of complex numbers by distributing the negative sign across the terms in the parentheses.
(4 + 1i) - (-6 + 4i) can be rewritten as:
4 + 1i + 6 - 4i
Next, we can combine like terms by adding the real parts (the numbers without the "i" term) and the imaginary parts (the numbers multiplied by "i") separately.
For the real parts, we have 4 + 6 = 10.
For the imaginary parts, we have 1i - 4i = -3i.
Therefore, the expression (4 + 1i) - (-6 + 4i) simplifies to:
10 - 3i
So the result of the expression is 10 - 3i.
It is important to note that "i" represents the imaginary unit, which is defined as the square root of -1. In complex numbers, the real part represents the real number component, and the imaginary part represents the multiple of the imaginary unit.
the expression represents the subtraction of two complex numbers, resulting in a new complex number with a real part of 10 and an imaginary part of -3i.
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A table is on sale for 68% off. The sale price is $147.20.
What is the regular price?
Answer:
Let's use "P" to represent the regular price of the table.
If the table is on sale for 68% off, then the sale price is 100% - 68% = 32% of the regular price.
We know that the sale price is $147.20, so we can write:
0.32P = $147.20
To find P, we need to divide both sides of the equation by 0.32:
P = $147.20 / 0.32
P = $460.00
Step-by-step explanation:
Answer:
$460 is the correct answer.
what is the answer to -4√14·2√8
Can someone help with measuring mass
the question is
1 . Compare the following measurements and insert <,> or = symbol.
4.5 kg ______ 150 cm
Answer: 4.5 km>150 cm
Step-by-step explanation:
I think you meant km, because kilograms are not compatible with cm, unless it's kg/m to g/cm.
Kilometers are units of measurement, and so are centimeters, so It'd be accurate only then.
Here's a box plot that summarizes the number of pens in each student's desk. A horizontal boxplot is plotted along a horizontal axis marked from 0 to 14, in increments of 1, labeled Number of pens. A left whisker extends from 0 to 2. The box extends from 2 to 6 and is divided into 2 parts by a vertical line segment at 4. The right whisker extends from 6 to 12. All values estimated. A horizontal boxplot is plotted along a horizontal axis marked from 0 to 14, in increments of 1, labeled Number of pens. A left whisker extends from 0 to 2. The box extends from 2 to 6 and is divided into 2 parts by a vertical line segment at 4. The right whisker extends from 6 to 12. All values estimated. Find the interquartile r
The interquartile range of this data set is equal to 4.
What is an interquartile range?In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 6 - 2
Interquartile range (IQR) of data set = 4.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The director of surgery at a local hospital is interested in understanding his unit’s costs. An assistant collected data for the past 36 months on unit cost (labor, supplies, and so on) along with the number of procedures performed in the unit. The assistant analyzed the data using a spreadsheet program, and the following output was generated.
Equation
Intercept $ 1,003,000
Coefficient on procedures $ 215
Statistical data
Correlation coefficient 0.503
R2 0.253
The unit is planning to perform an average 17,000 procedures per month for the coming year.
To make informed decisions about budget allocation and cost management, the director should consider this relationship between the number of procedures and unit cost.
The director of surgery at a local hospital aims to understand the unit's costs by analyzing data from the past 36 months, including unit cost (labor, supplies, etc.) and the number of procedures performed.
The assistant used a spreadsheet program to analyze this data and obtained an R2 value of 0.253.
This indicates that 25.3% of the variation in unit cost can be explained by the number of procedures performed. The unit plans to perform an average of 17,000 procedures per month in the upcoming year.
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