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July 31, 2014

Search: Estimate the area under the graph of f(x) = 10 cos(x) from x = 0 to x =

Number of results: 25,902

calculus
given the graph of f(x) = x sinx, 0<=x<=2pi assuming that a quantity y changes at a rate of y' = xsinx, find by how much it will increase or decrease over 3pi/2 <= x <= 2pi the area under the graph from 0 to pi/2 is 1 the area under the graph from pi/2 to pi is pi-...
September 27, 2011 by Ethan

Calculus
Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles. b. Sketch for yourself the graph of f and the rectangles. Is this left sum an overestimate or underestimate? Enter OVER or UNDER. c. Now use 5 right rectangles to estimate the area. ...
April 12, 2013 by Daniel

Calculus
Set up a Riemann sum to estimate the area under the graph of f(x) = 5x 2 + 2 between x = 0 and x = 1 using 3 subdivisions and left endpoints. Draw the graph and the 3 rectangles
December 5, 2012 by Rudy

Math: Need Answer to study for a quizz. Help ASAP
Estimate the area under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under the curve on [1,3] using a definite ...
November 18, 2010 by Jesse

Math
Estimate the are under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under the curve on [1,3] using a definite integral.
November 18, 2010 by Jesse

Calculus
Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles?
April 12, 2013 by Molly

Calculus
Use 5 right rectangles to estimate the area of the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles?
April 12, 2013 by Molly

Calc
Estimate the area under the graph of f(x)= x^2 + 2 x from x=4 to x=10 using 3 approximating rectangles and left endpoints.
April 22, 2009 by Perry

Calculus
Use n = 3 subdivisions and left endpoints to estimate the area under the graph of f(x) = 3x 2 + 1 between x = 0 and x = 1.
December 5, 2012 by Rudy

Calculus
Use n = 6 subdivisions and left endpoints to estimate the area under the graph of f(x) = 2x + 1 between x = 0 and x = 3.
December 5, 2012 by Rudy

calculus
4. a. Estimate the area under the graph of f(x)=sqrt(x^2+4) from x=0 to x=2 using four rectangles and right endpoints.
July 21, 2011 by Rick

Math: Calculus
Estimate the area under the graph of f(x)=3x^3+5 from x=-1 to x=4, first using 5 approximating rectangles and right endpoints, and then improving your estimate using 10 approximating rectangles and right endpoints. I'm having problem with using the midpoint to find the area. ...
November 12, 2010 by REALLY NEED HELP!!!!

Math
Use the following table of values to estimate the area under the graph of f(x) over [0, 1] by computing the average of R5 and L5. Table: x: 0 0.2 0.4 0.6 0.8 1 f(x): 51 48 46 43 41 38 I need help with this problem.
July 1, 2010 by Jason

Calculus
I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions? f is the differentiable function whose graph is shown in the figure. The position at time t (sec) of a particle moving ...
May 20, 2007 by Anonymous

physics
The first graph you plotted is called a speed-time graph. However, information other than speed or time can be obtained from such graphs. (a) What does the area under the line of the graph represent? the distance traveled? (b) Write an equation to represent the area under the ...
October 21, 2007 by Anonymous

Algebra 1B
A painter can use the formula A=2/3bh to estimate the Area of space under the parabola, where b is the length of the base and h is the height from the base to the vertex. Calculate the area, in square feet under each arch.
April 2, 2013 by Frank J

Calculus
Question Details: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the graph of f(x) = 8 + 2x2 from x = -1 to x = 2 using three rectangles and right end-points. R3 = 1 Improve your estimate by using six rectangles. R6 = 2 (b) Repeat ...
April 26, 2010 by Cindy

Math: Calculus
Estimate the area under the graph of f(x)=x^2+2x from x = 4 to x = 10 using 3 approximating rectangles and left endpoints. I got 290.25 as my answer but it's wrong. Would someone explain to me how to answer this question.
November 12, 2010 by REALLY NEED HELP!!!!

Calculus
Estimate the area under the graph of f(x) = 2x^3 + 3 from x= -1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the left and right endpoints, is there a ...
November 10, 2009 by Z32

Python programming
A standard problem in mathematics is to measure the area under a curve (or to integrate the function defining the curve). A simple way to do this is to approximate the area with a series of rectangles (whose areas are easy to compute). For example, we could split the range ...
January 13, 2013 by Anonymous

Calculus
The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim n → ∞ [f(x1)Δx + f(x2)Δx + . . . + f(xn)Δx] Use this definition to find an expression for the ...
November 24, 2013 by christina

Calculus
Estimate the area under the curve f(x)=x^2 between x=0 and x=1 using 4 rectangles of equal width if a) The height is taken from the right endpoint b) The height is taken from the midpoint. I have no idea what exactly this question is asking me to do is this suppose to be a bar...
March 11, 2012 by Enrique

Calculus-Approximate areas
Estimate the area under the graph of f(x)= x^2 + 3 x from x=1 to x=10 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoints: b) right endpoints:
November 4, 2013 by Liz

hi calculus asap
the graph of a piecewise linear function f, for -1<x<4. what is the value of integral (-1 to 4) F(x) dx? the interval i gave is grerater than or equal to and less than and equal to. i didn't know how to put the underscore under the symbol. for the integral, -1 is on the ...
November 30, 2006 by Anonymous

Calculus-Aproximate Areas
Estimate the area under the graph of f(x)=sin(pix) from x=0 to x=1 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve at a) left endpoint: b) right endpoint:
November 4, 2013 by Liz

Calculus-Aproximate Areas
Estimate the area under the graph of f(x)=sin(pix) from x=0 to x=1 using the areas of 3 rectangles of equal width, with heights of the rectangles determined by the height of the curve a a) left endpoint: b) right endpoint:
November 4, 2013 by Liz

Pre-Calc
Can anyone help with the following problem please...Thank u so much Let f(x) =|9x|. For the area above the x-axis and between the lines x= -9 and x=18 a. draw and label a sketch with the area shaded b. find the area of the region in the xy-plane under the graph of f(x)
December 8, 2010 by Amy

Calculus
a) Estimate the area under the graph of f(x)=7+4x^2 from x=-1 to x=2 using three rectangles and right endpoints. R3= ???? Then improve your estimate by using six rectangles. R6= ????? Sketch the curve and the approximating rectangles for R3. Sketch the curve and the ...
April 23, 2014 by TANYA

Calculus Help Please Urgent!!!
a) Estimate the area under the graph of f(x)=7+4x^2 from x=-1 to x=2 using three rectangles and right endpoints. R3= ??? Then improve your estimate by using six rectangles. R6= ??? Sketch the curve and the approximating rectangles for R3 and R6? b) Repeat part (a) using left ...
April 26, 2014 by Anonymous

Calculus
Estimate the area under the graph f(x)=3x^3 + 5 from x=-1 to x=5 using 12 mid points? I got the right answer for using 6 mid points but what mid points would I use for 12?
April 20, 2010 by Z32

Pre-calc
Can someone please show me the steps to this problem...Thanks in advance. Let f(x) = 9x. For the area above the x-axis and between the lines x= -9 and x=18 a. draw and label a sketch with the area shaded b. find the area of the region in the xy-plane under the graph of f(x)
December 7, 2010 by Amy

Math
Melvin estimate 645 + 322 by adding 600 + 300. Is his estimate sum an over or under estimate please? Ty
September 15, 2011 by Kelly

science/math
I have to make this density graph on a standard sheet of graph paper of this area outside. Each side of the area is a meter (in real life). What would be an good scale to use for my graph on graph paper?
September 26, 2008 by Jasmine

calculus
A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area.
March 2, 2008 by Anonymous

algebra
y= -x^2-12x+28 A painter can use the formula A=2/3bh to estimate the area of space under the parabola. Calculate area in square ft under each arch ~ if there are 8 arches to be painted how many square ft must be painted ~ if 1 gallon paints 200 square ft , how many gallons ...
March 31, 2013 by nancy

calculus
A rectangle with its base on the x-axis is to be inscribed under the graph of y=2-x^2. Find the height of the rectangle if the area is the largest possible area. (Round to the nearest hundreth)
November 13, 2011 by Sarah

Physics
On a postition versus time graph to find the acceleration you would simply find the area under the graph right? and how would you figure out whether acceleration is increasing, decreasing, constant of unknown from a graph? My guess is that the accereration is constant throughout.
September 21, 2007 by Tammy

calculus
The graph of f'(x) is shown for 0=< x =<10. The areas of the regions between the graph of f' and the x-axis are 20, 6, and 4, respectively. I'm going to describe the graph of f' since I can't post pictures. The first section of the graph goes up (like the sin function) ...
May 2, 2011 by Mike

Physics
What does the area under a velocity vs. time graph represent??
September 18, 2009 by Layla

Calculus
Find the area cut off by x+y=3 from xy=2. I have proceeded as under: y=x/2. Substituting this value we get x+x/2=3 Or x+x/2-3=0 Or x^2-3x+2=0 Or (x-1)(x-2)=0, hence x=1 and x=2 are the points of intersection of the curve xy=2 and the line x+y=3. Area under curve above X axis ...
April 1, 2014 by MS

Math
Jenna lives 4 3/10 miles from school, she estimates that she travels 4 x2x5 or 40 miles each week. Is her estimate an over estimate or underestimate? I think it is under estimate but not sure?
February 12, 2013 by Jared

calculus
Find the area of the region under the graph of the function f on the interval [-1, 2]. f(x) = 6x + 1
December 8, 2010 by Anonymous

Calculus
Let R be the region in the first quadrant under the graph of y=1/sqrt(x) for 4</=x</=9. (a)Find the area of R. I took the antideriative. Then, I plugged in the 9 and 4. I got 2. (b) If the line x=k divides the region R into two regions of equal area, what is the value of...
December 13, 2007 by Anonymous

6th G-Math
1.What is a reasonable estimate for the area of a circle with radius 4 cm? A. Area=12cm^2 B. Area=16cm^2 C. Area=24cm^2 D. Area=48cm^2
April 9, 2012 by Lauren

Algebra 2 Need Help
1. function g(x)=-x^2-3x+7 . Find the area under the curve for the domain 4 x 1. a 71.6 square units b. 46 square units c.35.83 square units d.17.916square units 2. y=2sin(circle with a line through it) a. How many cycles occur in the graph? b. Find the period of the graph...
August 5, 2012 by Anonymous

algebra
The drama club is building a backdrop using arches whose shape can be represented by the function f(x)=-x^2+2x+8, where x is the length in feet. The area under each arch is to be covered with fabric. -What is the length of the segment along the floor of each arch? -What is the...
May 8, 2008 by astrid

integration
Find the area of the region under the graph of the function f on the interval [-1, 2]. f(x) = 6x + 1 bound by the x axis
December 8, 2010 by peter

calculus(Lab)
Well, first graph the graph of f(x)=-1/10x^2 + 3 2. We are going to approximate the area between f and the x-axis from x = 0 to x = 4 using rectangles (the method of Riemann sums). This is not the entire area in the first quadrant, just most of it. Draw four inscribed ...
January 25, 2012 by Yoona

math
Find the area of the region under the graph of the function f on the interval [4, 10]. f(x)=10x-5 ? square units
November 30, 2012 by Ashton

Calculus
Use a simple area formula from geometry to find the area under function A(x) that gives the area under the function f(x) = 9 on the interval [2, x].
December 19, 2010 by Raj

physics
the slope of a velocity-time graph represents? the area under a velocity time-graph represents? the slope of a line drawn tangent to a curved position-time graph represents..?
September 14, 2009 by kaaay

calculus
The approximation to the area under the graph of the function f(x)= 1/(1+x^2) on the interval [-1,1], using four rectangles and the midpoint rule is
April 7, 2011 by Anonymous

math
Find the area of the region under the graph of the function f on the interval [-27, -1]. f(x)= 2-3square root x ? square units
December 6, 2012 by Britney

Calculus
If 0 <= k <= pi/2 and the area of the region in the first quadrant under the graph of y = 2x-sinx from 0 to k is 0.1, then k = (a) 0.444 (b) 0.623 (c) 0.883 (d) 1.062 (e) 1.571
December 21, 2012 by Anonymous

algebra
Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. Find the area of a rectangle if three of its corners are (-0.1,-3.4), (-7.9,-3.4), and (-0.1,6.8). one I draw the graph how do I figure out the area of the...
February 28, 2011 by bianca

Calculus - maximum problem
An isosceles trapezoid is inscribed under the graph oof y =cos x. what are the dimensions which will give the greatest area?
October 26, 2009 by calculus

calculus
Let A be the area if the region in the first quadrant under the graph of y = cos(x) and above the line y = k for 0 < k < 1. a. Determine A in terms of k. b. Determine the value of A when k = 1/2 c. If the line y = k is moving upward at a rate of 1/pi units per minute, at...
March 23, 2010 by mary

Calculus
Consider the function x^2+x-4 Estimate the area between the graph and the x-axis between x=2 and x=4 using four rectangles and right end points.
December 17, 2013 by Lindsay

calculus
Estimate the area of the region under the curve y = ln(x) for 1 ≤ x ≤ 4. Use the left hand rule with n = 50. Give your answer to four decimal places.
November 19, 2009 by Dana

Calculus
Estimate the area of the region under the curve y = ln(x) for 1 ≤ x ≤ 4. Use the left hand rule with n = 50. Give your answer to four decimal places.
November 19, 2009 by Dana

calculus
Estimate the area of the region under the curve y = ln(x) for 1 ≤ x ≤ 5. Use the left-hand rule with n = 50. (Round your answer to four decimal places.)
November 14, 2011 by Anonymous

Calc.
Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under the tangent. Find out...
September 26, 2006 by Hebe

CALC
Let f(x) be the function e^sin(x/10). If you wanted to estimate the area under the curve for this function from 3 to 5, how many intervals would you need to use to be sure that your upper and lower bounds differered by no more than .01?
January 30, 2008 by anonymous

math
Graph y = x^2 x +3 for 0≤x≤6 (b) Calculate the mid- ordinates for 5 strips between x = 1 and x 6, and hence use the mid-ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x- axis. (c) assuming that the area determined by ...
June 3, 2012 by Anonymous

math
Graph y = x^2 x +3 for 0≤x≤6 (b) Calculate the mid- ordinates for 5 strips between x = 1 and x 6, and hence use the mid-ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x- axis. (c) assuming that the area determined by ...
June 5, 2012 by Anonymous

Math
Graph y = x^2 x +3 for 0≤x≤6 Calculate the mid- ordinates for 5 strips between x = 1 and x 6, and hence use the mid-ordinate rule to approximate the area under the curve between x = 1, x = 6 and the x- axis. assuming that the area determined by integration to ...
April 14, 2013 by Anonymous

calculus -- PLEASE HELP!
Suppose you are trying to evaluate the intergral 2x^3dx and you make the substitution u=x^2. The substitution takes one area and converts it to a different one-in this case a trapezoid with vertical sides. Denote by R the region under the first curve from 3 to 3.01 and ...
January 30, 2008 by anonymous

calculus
How do you estimate derivatives when you don't know the actual equation of the line on the graph, but you have just a picture of the graph?
October 3, 2011 by fr

calc: relative error
The circumference of a sphere was measured to be 77 cm with a possible error of .8 cm. Use differentials to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area. please help me..thank you! Area= 4 PI radius^2 dA...
October 31, 2006 by amanda

math
1. Estimating the Temperature of a Yam Suppose you put a yam in a hot oven, maintained at a constant temperature of 200C. As the yam picks up heat from the oven, its temperature rises.16 (a) Draw a possible graph of the temperature T of the yam against time t (minutes) since ...
September 29, 2011 by Anonymous

Physics
In Figure 10-20, the magnitude of the force necessary to stretch a spring is plotted against the distance the spring is stretched. Figure 10-20 (a) Calculate the slope of the graph, k, and show that F = kd, where k = 25 N/m. (b) Find the amount of work done in stretching the ...
October 25, 2011 by Claire

Calculus
These are the two problems from my homework I don't get.. can you help me? A: y=2x-x^3 [0,1] use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval. Sketch the region B: f(x)=4-(12/(x^2))Calculate the lower...
December 5, 2011 by Wesley

Single Variable Calculus
find an expression for the area under the graph of f(x)= (x^2)+x from x=2 to x=5 as a limit of a riemann sum (do not need to evaluate). the answer i got was: lim as x-> infinity of sigma from i=2 to n of (2+3i/n)^2+(3i/n)(3/n) is this correct?
August 11, 2011 by Kelly

calculus II
We're doing areas by integrals now, with 2 eqns. I have a few questions. 1. Sketch the region in the xy-plane defined by the inequalities x-2(y^2)> 0 and 1-x-abs(y)>0. and find its area. Would it be best to solve for x, then graph it as x= something? Then find the ...
February 8, 2007 by Shelley

math (4)
Sketch the graph (Do this on paper. Your teacher may ask you to turn in this graph.) and find the area of the region bounded below by the graph of the function and above by the x axis from x = 0 to x = 1. f(x) = -xe^(-x^2) x=0 x=1
April 23, 2014 by Vanessa

math (4)
Sketch the graph (Do this on paper. Your teacher may ask you to turn in this graph.) and find the area of the region bounded below by the graph of the function and above by the x axis from x = 0 to x = 1. f(x) = -xe^(-x^2)
April 24, 2014 by Vanessa

math (4)
Sketch the graph (Do this on paper. Your teacher may ask you to turn in this graph.) and find the area of the region bounded below by the graph of the function and above by the x axis from x = 0 to x = 1. f(x) = -xe^(-x^2)
April 25, 2014 by Mia

algebra
Solve the equation x2 + 8x 2 = 0 using both a. The quadratic formula b. Completing the square Write a paragraph or two comparing and contrasting the two methods. Explain which method you prefer and why. c) Use the accompanying graph to estimate the time at which the workers ...
January 3, 2011 by carolyn

Geometry
graph each set of lines to form a triangle. find the area and perimeter. y=2, x=5 , and y=x Answer is Area = 4.5 units Perimeter = 6 + square root of 2. I don't know how to graph this. What does y=x mean?
July 4, 2012 by Ethan

Calculus
Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. Let R be the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line tangent to the graph of f at x=0. Graph shown through...
February 27, 2013 by Jessy152

Precalculus
f(x)=x^2-1 Graph the function. Estimate the intervals on which the function is increasing or decreasing, and estimate any relative maxima or minima.
June 25, 2013 by Lacresha

calculus help lttle question
find the area of the regin bounded by the graphs of y=-x^2=2x=3 and y=3. i don't need help solving the problem and but i am a little confused. ok the graph is a parabola and i drew a parobla with y= 3. now when find the area, am I finding the area on the top, above y=3 or on ...
January 8, 2007 by david

calculus
a particle moves along the x-axis (units in cm) its initial position at t=0 sec is x(0)=15. the figure shows the graph of the particle's velocity v(t). the numbers are areas of the enclosed regions. in the graph 0 to a is 4 under the x-axis, a to b is 5 above the x-axis, b to ...
April 28, 2010 by shelby

math analysis
A rectangle with its base on the x axis is to be inscribed under the positive portions of the graph of y=8-x^2 . Write an equation for the area of the rectangle which uses only the variable x.
October 31, 2011 by sarah

physics
A car travels on a straight road for 40km at 30km/h. It then continues in same direction for 40km at 60km/h. a)What is the average velocity of the car during the 80km trip?(assume it moves in positive x direction) b)What is the average speed? c)graph adn indicate how average ...
September 10, 2006 by sara

Calculus
The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area? Also Estimate the relative error in the calculated surface area.
November 7, 2009 by Salman

Calculus
The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area? Also Estimate the relative error in the calculated surface area.
November 8, 2009 by Salman

CALCULUS
The circumference of a sphere was measured to be 83000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. ________________ Estimate the relative error in the calculated surface area. _________________
May 19, 2012 by Sarah

Calculus
The circumference of a sphere was measured to be 88000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.
February 19, 2010 by John

calculus
The circumference of a sphere was measured to be 78.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.
August 28, 2010 by jin

CAL
THe circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use the linear appoximation to estimate the maximum error in the calculated surface area. and estimate the relative error in the calculated surface area.
July 19, 2011 by tony

math
The circumference of a sphere was measured to be 82.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area.
March 28, 2012 by bobby

Cal
The circumference of a sphere was measured to be 86.000 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area and Estimate the relative error in the calculated surface area.
February 24, 2011 by Kong

cal
The circumference of a sphere was measured to be 86.000 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area and Estimate the relative error in the calculated surface area.
March 1, 2011 by KOng

annie
You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You estimate that a transmission wire is about 11m above the ground. The local power company tells you that the line operates at 13kV and provide a maximum of 86MW to the local area. ...
December 14, 2009 by physics help

calculus
suppose that the area under the curve y=1/x from x=a to x=b is k. the area in terms of k, under the curve y=1/x from x=2a to x=2b? justify
February 23, 2010 by Anonymous

Calculus
Approximate the area under the graph of f(x)and above the x-axis using 4 rectangles: f(x)=x(x) +2 using 4 rectangles at intervals 0,5
December 2, 2010 by Rod

Math
A shoe manufacturer determines that the annual cost of making x pairs of one type of shoe is $30 per pair plus $100,000 in fixed overhead costs. Each pair of shoes that is manufactured is sold wholesale for $50. a. Find the equations that model Revenue and cost and graph each ...
March 15, 2010 by Rony

Math
Use a radius of 50 and 3 for pi to estimate the area. Then use a radius of 40 and 3 for pi to estimate the area. Is your answer reasonable? Why?
March 7, 2012 by Laurie

math
A government survey conducted to estimate the mean of houses in a metropolitan area is designed to have a margin of error of 10,000. Pilot studies suggest that the population standard deviation is 70,000. Estimate the minimum sample size needed to estimate the population mean ...
June 5, 2014 by Erma

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