The value of the triple integral is 1920pi/3.
Here are five other iterated integrals that are equal to the given iterated integral:
[tex]\Integral^2_0 \Integral^y_0 \Integral^1_0 f(x, y, z) dx dy dz[/tex]
[tex]\Integral^2_0 \Integral^z_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]
[tex]\Integral^1_0 \Integral^y_0 \Integral^1_z f(x, y, z) dx dz dy[/tex]
[tex]\Integral^1_0 \Integral^z_0 \Integral^1_y f(x, y, z) dx dy dz[/tex]
[tex]\Integral^z_0 \Integral^1_0 \Integral^y_z f(x, y, z) dx dy dz[/tex]
To evaluate the triple integral of[tex](4 + 5x^2yz^2) dV[/tex]over the cylindrical region [tex]x^2 + y^2[/tex] <= 4, -2 <= z <= 2, we can use geometric interpretation and symmetry.
Note that the integrand [tex](4 + 5x^2yz^2)[/tex] is an even function of x and y, and an odd function of z.
Therefore, the integral over the region where z is positive is equal in magnitude but opposite in sign to the integral over the region where z is negative.
Hence, we can evaluate the integral over the region 0 <= z <= 2, and then double the result.
The region of integration is a cylinder of radius 2 and height 4.
Since the integrand is not dependent on x and y, we can factor out[tex](4 + 5z^2)[/tex] from the integrand, and evaluate the remaining integral over the unit disc in the x-y plane.
Thus, the triple integral can be written as:
[tex]8 * \Integral^2_0 \Integral^2pi_0 \Integral^2_0 (4 + 5z^2) r^3 sin(\theta) dr d(\theta) dz[/tex]
Integrating with respect to r from 0 to 2 and with respect to [tex]\theta[/tex] from 0 to [tex]2\pi[/tex], we get:
[tex]8 * \Integral^2_0 \Integral^2pi_0 (4 + 5z^2) sin(\theta) d(\theta) dz[/tex]
Integrating with respect to theta from 0 to 2pi, we get:
[tex]16pi * \Integral^2_0 (4 + 5z^2) dz[/tex]
Integrating with respect to z from 0 to 2, we get:
16pi * (32/3 + 80) = 1920pi/3.
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6PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
b. 8/17
Step-by-step explanation:
hope this helps ;)
The ratio of girl to boys in mr Day class is 3 to 5 . If there is 15 boys in mr Day class how many more boyz are there then girls
Answer:
If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:
15 boys - 9 girls = 6 more boys than girls.
Step-by-step explanation:
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Question in picture!!
I have more questions on my account if you can help!!
We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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Jerome is a photographer. He earns $125 per hour
(d) Part D
Create a graph of the data from the table.
The graph of the data from the table is added as an attachment
Creating a graph of the data from the table.From the question, we have the following parameters that can be used in our computation:
Jerome is a photographer. He earns $125 per hour
This means that the equation of the function is
f(x) = 125x
Where x is the number of hours he works
Using the above as a guide, we have the following table of values
x f(x)
1 125
2 250
3 375
4 500
5 625
6 750
Next, we plot the graph from the table of values and the function f(x) = 125x
The graph of the function is added as an attachment
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Help it a screenshot
The equation will be w = 40b
How do you formulate an equation for the scenario provided?To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b
This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).
The above answer is based on the information below as seen in the picture;
Yuki works at a garden store. She is stacking 40 pounds bags of soil.
write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.
+ - . = b, w, 40
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HELP WILL GIVE BRAINLIEST GEOMETRY SHOW WORK
The surface area of the right prism is 192.9 m².
What is a prsim?A prism is a solid shape that is bound on all its sides by plane faces.
To calculate the surface area of the prism, we use the formula below
Formula:
S.A = bh+L(b+h+c)................. Equation 1Where:
S.A = Surface area of the prismb = Base of the triangular baseh = Height of the triangular baseL = Length of the prismc = Hypotenus of the triangular baseFrom the diagram in the question,
Given:
b = 3 mh = 8 mc = 8 mL = 9.1 mSubstitute these values into equation 1
S.A = (3×8)+9.1(3+8+8)S.A = 24+172.9S.A = 192.9 m²Hence, the surface area is 192.9 m².
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the average score of 100 students taking a statistics final was 70, with a standard deviation of 7. assuming a normal distribution, what test score value separates the top 2.5% of the students from the rest of the students? (show your work)
The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.
To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.
z = (x - μ) / σ
To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.
Presently ready to utilize the z-score equation to unravel for x:
1.96 = (x - 70) / 7 Increasing both sides by 7, we get:
x - 70 = 13.72
Including 70 to both sides, we get:
x = 83.72
Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.
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A quadrilateral has vertices P(-5,7), Q(-3,6), and R(-6,0). Which point would make PQRS a rectangle?
~a.) S(-4,-1)
~b.) S(-7,2)
~c.) S(-8,2)
~d.) S(-8,1)
From the given information about the vertices of the quadrilateral, the point at which the PQRS quadrilateral will be made a rectangle is S(17/14, -1/7).
What is a quadrilateral? What are its properties?A quadrilateral is a four-sided polygon, which means it's an unrestricted shape with four straight sides.The parcels of a quadrilateral include Four sides A quadrilateral has four sides.The sum of the angles in a quadrilateral is always 360 degrees.Each type of quadrilateral has its own unique set of parcels and characteristics.Perimeter The border of a quadrilateral is the sum of the lengths of its sides.Area The area of a quadrilateral can be calculated using colorful formulas, depending on the type of quadrilateral and the information given about its sides and angles.What is a rectangle? What are its properties?An example of a quadrilateral with all four angles at right angles (90 degrees) and opposite sides that are parallel and of equal length is a rectangle.The characteristics of a rectangle are as follows: 4 right angles: A rectangle has four angles, and all four of them are right angles, which means they are all 90 degrees.A rectangle's perimeter is determined by adding the lengths of its four sides, which is equal to twice the length plus twice the width.Area: The length times the breadth of a rectangle equals the area of that shape.Perpendicular sides are opposite sides: A rectangle's opposite sides are perpendicular to one another, therefore when they intersect, they do so at a right angle.Parallelograms include rectangles as well: since a rectangleWe need to find the point that would make PQRS a rectangle. We will first determine the fourth vertex S which, when connected to the remaining three vertices, forms a quadrilateral with four right angles.As opposite sides of a rectangle are parallel and equal in length, we can first find the lengths of PQ and RS, which should be equal in a rectangle.From the distance formula, we have:PQ = [tex]\sqrt{6-7)^{2}} +(-3+5)^{2} =\sqrt{[2^{2}+(-2)^{2} } =\sqrt{8}[/tex]RS = [tex]\sqrt{(0 - 6)^2+ (-5 + 3)^2} + \sqrt{[(-6)^2 + (-2)^2] }= \sqrt40}[/tex]The midpoint of PQ is: [tex][(6 - 5)/2, (-3 - 3)/2] = (0, -3)[/tex]The slope of PQ is: [tex](6 - 7)/(-3 + 5) = -1/2[/tex]The equation of the perpendicular bisector of PQ is:[tex]y + 3 = 2(x - 0) or y = 2x - 3[/tex]The midpoint of RS is: [tex][(0 - 6)/2, (-5 - 0)/2] = (-3, -5/2)[/tex]The slope of RS is: [tex](0 - 6)/(-5 + 3) = 3[/tex]The equation of the perpendicular bisector of RS is :[tex]y + 5/2 = (-1/3)(x + 3) or y = (-1/3)x - 1/6[/tex]Now to find the intersection of these two lines, we can set them equal to each other and compute the value for x:[tex]2x - 3 = (-1/3)x - 1/6[/tex][tex]12x - 18 = -2x - 1[/tex]Adding 2x and 18 to both sides gives:[tex]14x = 17x = 17/14[/tex]To find the y-coordinate of the intersection, substitute x into either equation:[tex]y = 2(17/14) - 3 = 1/7[/tex]So, the point that would make PQRS a rectangle is S(17/14, -1/7).To know more about polygons visit:
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The answer is option c.) S(-8,2).
What is quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
For PQRS to be a rectangle, its opposite sides must be parallel and have equal length. We can find the length of PQ and RS using the distance formula:
PQ = √[(Qx - Px)² + (Qy - Py)²]
= √[(-3 - (-5))² + (6 - 7)²]
= √[4 + 1]
= √[5]
RS = √[(Sx - Rx)² + (Sy - Ry)²]
= √[(-8 - (-6))² + (2 - 0)²]
= √[4 + 4]
= √[8]
Since PQ and RS are not equal, we need to find a point S such that PQRS has equal sides. Moreover, the diagonals of a rectangle bisect each other. Hence, we can use the midpoint formula to find a point that bisects PR:
M = [(-5 - 6)/2, (7 + 0)/2]
= (-11/2, 7/2)
Let's consider each option:
a.) S(-4,-1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-4, -1) cannot be a point of RS.
b.) S(-7,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-7 + 6) = -2, so S(-7, 2) cannot be a point of RS.
c.) S(-8,2)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-8, 2) could be a point of RS. Moreover, the distance from S to the midpoint of PR is:
√[(-11/2 - (-8))² + (7/2 - 2)²]
= √[25/4 + 9/4]
= √[34]/2
This is equal to the length of PQ, so PQRS could be a rectangle with S(-8, 2).
d.) S(-8,1)
The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (1 - 0)/(-8 + 6) = -1, so S(-8, 1) cannot be a point of RS.
Therefore, the answer is option c.) S(-8,2).
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ey of the
1
11. The table shows the wages of a worker in
an office. Which equation can be used to
represent how much, y, the worker earns in x
hours?
Hours
2
CIT
4
10
6
10
A. y = 20x+ 5.50
B. y = 10x + 5.50
C. y = 20.5x
Dy = 10x
Wages
$25.50
$45.50
$65.50
$105.50
12. Carlisle is going to paint his living room
Answer:
To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:
Change in wages = $105.50 - $25.50 = $80
Change in hours = 6 - 2 = 4
Rate of pay per hour = Change in wages / Change in hours
= $80 / 4
= $20
Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:
y = $20x
Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.
Step-by-step explanation:
On a piece of paper, use a protractor to construct a triangle with angle measures of 40° and 60º.
What is the measure of the third angle?
Responses
60°
80°
100°
180°
The measure of the third angle in the triangle is 80 degrees.
What is the measure of the third angle?The sum of the angles in a triangle is always 180 degrees.
Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,
We can subtract the sum of these two angles from 180°:
180° - (40° + 60°) = 180° - 100° = 80°
Therefore, the measure of the third angle in the triangle is 80 degrees.
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3PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer: x= 7191.509 ft
Step-by-step explanation:
Sin9/1 = 1125/x
X/1 = 1125/sin9
Altogether the Green Team jumped 10264 times. The Yellow Team did 759 fewer jumps than the Green Team. How many jumps did the Yellow Team do?
Can somebody help me out?
Answer:
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.
what is the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet?
The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet, we need to use the formula:
Work = Force x Distance
In this case, the force is the weight of the crate, which is 30 pounds. The distance is the height the crate is lifted, which is 3 feet.
So, Work = 30 pounds x 3 feet
We can simplify this by converting pounds to foot-pounds, which is the unit used to measure work. To convert pounds to foot-pounds, we need to multiply the weight by the distance. So:
Work = 30 pounds x 3 feet = 90 foot-pounds
Therefore, the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.
To calculate the amount of work done, in foot-pounds, for lifting a crate weighing 30 pounds a total of 3 feet, you can follow these steps:
Step 1: Identify the weight of the crate (30 pounds) and the distance it is lifted (3 feet).
Step 2: Multiply the weight of the crate by the distance lifted.
Work (in foot-pounds) = Weight (in pounds) × Distance (in feet)
In this case:
Work = 30 pounds × 3 feet
Work = 90 foot-pounds
So, the amount of work done is 90 foot-pounds.
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The work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is given by the formula:
Work = Force x Distance x cos(theta)
where Force is the weight of the crate, Distance is the vertical distance lifted, and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees in this case since the force is acting vertically upwards).
Therefore, the work done to lift a crate weighing 30 pounds a total of 3 feet is:
Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds
So the amount of work done to lift the crate is 90 foot-pounds.
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ADD: (Give answer in simplest form)
6 2/7+7 1/2
The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
r sin θ = 10
y = 10
x = 10
y = 10x
x = 10y
The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.
How to find the equation in rectangular coordinates
Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:
cos θ = x / r
sin θ = y / r
Where:
θ - Angle, in degrees. x, y - Legs of the right triangle.r - Hypotenuse of the right triangle.Then, the equation in polar coordinates is:
r · sin θ = 10
y = 10
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What is the factored form of x² + 5x+6?
The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)
How to determine the factorized formTo factorize the quadratic equation, we need to take the following steps;
Multiply the coefficient of the x squared by the constant value, we have;
6
Now, find the pair factors of the product that would add up to give 5, we have;
2 + 3
Substitute the values into the expression, we have;
x² + 2x + 3x + 6
Now, group the expression in pairs, we have;
(x² + 2x) + (3x + 6)
Factorize the expressions
x(x + 2) + 3(x + 2)
Then, we have;
x + 3
x + 2
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Find the volume of the figure below:
The volume of the cylinder is 3532.5 metres cube.
How to find the volume of a cylinder?The figure above is a cylinder. The volume of the cylinder can be found as follows:
volume of a cylinder = πr²h
where
r = radiush = heightTherefore, let's find the height using Pythagoras's theorem.
25² - 15² = h²
h² = 625 - 225
h = √400
h = 20 metres
Hence,
volume of a cylinder = 3.14 × 7.5² × 20
volume of a cylinder = 3532.5 metres cube
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The Orchard Cafe has found that about 4% of the diners who make reservations don't show up. If 81 reservations have been made, how many diners can be expected to show up
The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made
To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:
1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.
2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).
81 reservations x 0.96 (96% as a decimal) = 77.76
Since the number of diners must be a whole number, you can round the result to the nearest whole number.
In this case, 77.76 can be rounded down to 77.
Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.
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8 Find in degrees. 17 [?] degrees Round to the nearest hundredth.
Answer:
Θ ≈ 28.07°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )
Jordan reads a comic book at a rate of 21 pages in 6 minutes. At this rate, how many pages does he read each minute?
Answer:
x = 3.5 pages per minute
Step-by-step explanation:
We make the relationship
21 pages ------ 6 min
x pages -------- 1 min
So x= (21x1)/(6)
x = 3.5 pages per minute
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).
What is a median?The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.
A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.
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G(Q) = 5 + 3Q + 202 - Q2 C2(Q) = 3 + 4Q + 2 1. Find the MC function for both C1(Q) AND C2(Q). 2. Find AVC function for both Ci(Q) AND C2(Q). 3. Find AFC function for both C1(Q) AND C2(Q). 4. Find AC function for both Ci(Q) AND C2(Q). 5. Find ATC function for both Ci(Q) AND C2(Q).
For C1(Q) = 3 - 2Q.
For C2(Q) = 4.
2. The AVC function
For C1(Q) = 5/Q + 3 + 20/Q - Q.
For C2(Q) = 3/Q + 4 + 2/Q.
3. The AFC function
For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)
For C2(Q) = 0.
4. To find the AC function
For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5.To find the ATC function
For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)
For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
Find the ATC functions for C1(Q) and C2(Q) given the provided cost functions?
1. To find the MC function, we take the derivative of the cost functions with respect to Q.
For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.
For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.
2. To find the AVC function, we divide the cost functions by Q.
For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.
For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.
3. To find the AFC function, we subtract the AVC function from the ATC function.
For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)
= 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.
4. To find the AC function, we add the AVC function to the AFC function.
For
C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).
For
C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.
5. To find the ATC function, we divide the AC function by Q.
For
C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q
= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).
For
C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q
= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.
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You decide this is not enough time so you decide to ration your meals. You a
(75%) of each meal instead. So, one ration = 0.75 meals. How many total rati
ave?
meals
1 fails
The total rations will be: 0.75 times the number of meals.
How many rations will you have in total?A ration refers to the fixed portion of food or other goods allowed to each person in times of shortages.
In this context, If you decide to eat only 75% of each meal, that means you will consume 0.75 times the number of meals.
For example, if you originally had 100 meals, you will now have:
= 0.75 x 100
= 75 rations in total.
This approach allows to stretch your meals and make them last longer by rationing your food intake.
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As a candle burns, it decreases in height by 2 inches every hour. If the candle is 12 inches tall when it is lit, how will the height change over time? If the candle burned for 2 hours, how many inches tall will it be?
The height of the candle change over time as a linear function
How will the height of the candle change over time?The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.
We can write the equation for the height of the candle as:
h(t) = 12 - 2t
where h is the height of the candle in inches and t is the time in hours.
If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:
h(2) = 12 - 2(2) = 8
So the height of the candle after 2 hours of burning is 8 inches.
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Evaluate the expression when a = 3 and x = -7 .
-a + 9x
725 unit digit of (325)
The unit digit of 725 unit digit of (325) is given as 5
How to solve for the unit digitUnveiling the unit digit of a number raised to an exact power can be done by analyzing the pattern of the unit digits of said power sequence.
For instance, given the task of ascertaining the unit digit of 325^725, let us observe the recurrent pattern concerning 5's power line:
[tex]5^1 = 5\\5^2 = 25\\5^3 = 125\\5^4 = 625\\5^5 = 3125[/tex]
It is readily evident that the final digit of 5 raised to any affirmative integer power shall invariably remain as 5. Correlatively, the end figure for 325^725 is also 5.
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Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
By using slope intercept , These were the two points on the line: (0,-2) and (7,2).
Define slope intercept?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.
These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.
We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).
So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.
Graph given below:
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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 120 responses, but the responses were declining by 10% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 18 days after the magazine was published, to the nearest whole number?
The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.
What is meant by days?
Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.
Explain whole numbers
Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.
According to the given information
The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).
In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:
S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)
≈ 1200
So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.
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1. a small electronics store has begun to advertise in the local newspaper. before advertising, the long-term average weekly sales were $9,820. a random sample of 50 weeks while the newspaper ads were running gave a sample mean weekly sales of
The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.
To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.
The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:
H0: μ = $9820
The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:
Ha: μ > $9820
The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.
To calculate the test statistic, we can use the formula:
t = (X - μ) / (s / √n)
Where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:
s = θ / √n = $1580 / √50 = $223.61
Now we can calculate the test statistic:
t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45
Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.
Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.
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--The given question is incomplete, the complete question is given
" a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.
A. state the null and alternate hypothesis.
B. Compute the or t va;ue of the sample test statistic.
C. Find the critical value(s).
D. based on the answers to a-c, what is your conclusion?"--