A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are 0, 18, 58, 79, 94, 106, 117, 128, 63, 39, and 0. Use the Midpoint Rule with n = 5 to estimate the volume of the liver. Volume cubic centimeters

Q: Determine the area of the given region under the curve.

A: see the attached file for a detailed solution.

Q: e z score such that pz is less th

A: we are given that the probability value is 0.7880

Q: Estimate the area of the curve y = 2x + x - 3 from x = 1 to x = 3 by using 5 rectangles and right…

A: We have the lower limit, a = 1, and the upper limit, b = 3.  We are using five rectangles, that is n…

Q: find the Z score such that the area to the right of the Z- score is 0.0054.

A:

Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

Q: find the z-score that has 30.5 of the distribution's area to its left

A: Given, z-score = 30.5

Q: If the area of the shaded region. is 21.05% or .2105, find the z score at the question mark. Round…

A: z-score: The z-score is the number of standard deviations that the data points lies above or below…

Q: Find the sum of the areas of approximating rectangles for the area under f(x) = 48 – x², between x =…

A: Given: The function is  f(x)=48-x2   Formula used: A≈∑i=1n f(xi)∆x Where ∆x=b-an

Q: The area to the right of z-score of 0 is

A: We know that the Z is standard normal variate with mean 0 and variance 1  i.e. Z~N(0,1) Since the…

Q: A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line…

A:

Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 4-meter intervals as…

A: We have to calculate area using Mid point Rule.

Q: Find the area of the region bounded by the curve 2-4r and the lines x = 1 and x = 4.

A: To find the area

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and…

A:

Q: 2. Find the length of curve of shaded region in the shape. y = x2 2.

A:

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

A:

Q: For a z-score of 2.80, what is the area beyond the z-score in the tail?

A: The given z-score is 2.80.

Q: a. Determine the z-score such that the area to its right is 16%. = 2

A: The standard normal distribution is derived from the continuous probability distribution, i,e from a…

Q: use midpoints from [1,5] with n = 4 to approximate the area

A:

Q: Find two z values so that 53% of the middle area is bounded by them.

A:

Q: Use 6 rectangles to find estimates of each type of area under the given graph of f from x=0 to x=12…

A: Total interval length =12 No of rectangles = 6 Therefore each sub interval length = 2 Midpoints of…

Q: Find the average value of ƒ(x) = sqrt(x + 1)/ sqrt(x) on the interval [1, 3]

A: Given a function

Q: Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis

A: We have to find the area bounded by the curves.

Q: Compute the area of the region enclosed by the x-axis and the curve y = x3 - 7x2 + 10x

A:

Q: The area bounded by the curve y = 6x and the lines x = 9 ,x = 11 and x %3| axis is - O 486 square…

A: Consider the curves, y=6x,  x=9,  x=11   and   x-axis To draw the bounded region:

Q: What is the area of the region bounded by y = x^2, the x-axis, and the lines x = 2 and x = 5, using…

A: Given function is, y=x2 Limits for x is, x1=2x2=5

Q: Calculate the average height above the x-axis of a point in the region 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2.

A: Consider the given: To find:The average height above the x-axis of a point in the…

Q: Calculate the area of the region enclosed by y = x2 , lines x =1, x = 3, and the x − axis. Round up…

A:

Q: The area between a negative Z score and a positive Z score can be found by     adding the Z scores…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ  are the mean…

Q: The edge x of a cube is measured with an error of at most 0.5%.What is the maximum corresponding…

A:

Q: Find the indicated z-score shown in the graph to the right. Area = 0.1711 z=?0

A:

Q: find the z score area  z less than 2.5 z between 1.5 and -1.5

A:

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

A:

Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

A:

Q: b) Estimating the shaded area with the Composite Trapezoidal Rule with n=4 yields lunits2, while the…

A:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and…

A:

Q: Find Z Z score that corresponds to the cumulative area 0.0059

A:

Q: . Find the area bounded by y = (11 – x), the lines 3x=2, x=10, and the x-axis.

A:

Q: Find the Area bounded by the given curves. 1. у %3 х2, у32х+3 2. х2 - у -1, х3у -3 3. у 3 х2, у-2-х2

A:

Q: Find the area of the shaded region. (9,3) x = y2 (0,0) (9,-3)

A: Using horizonal strip Established double integral

Q: Find the average value over the given interval. 32) y = 5x2; [-1,2]

A: We can find the average value as below.

Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 3-meter intervals as…

A:

Q: Area = 0.2033 Z3D70

A: Using the given graph,

Q: The point estimate for p, p, is . (Round to three decimal places as needed.) The point estimate for…

A: total population = 4445 2735 think main stream media is more interested in making money than telling…

Q: ______  is the z-score such that the area under the curve to the left is 0.93

A: Given info: The area under the curve to the left is 0.93.

Q: The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate fOx) dx, wi

A:

Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson’s Rule with n = 4.

A: Definition used -             Trapezoidal Rule-                   ∫abf(x)dx≈∆x2(f(a)+…

Q: The area of the region bounded by x = /9- y2, the y-axi first quadrant is:

A: Here we have to find the area bounded by the region x=9-y2 .....................(1), the y-axis, and…

Q: find out z score shaded area between -1.5647 and 1.3698

A:

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.