answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
cupoosta
2 months ago
14

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obt

ained 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, 59, 78, 95, 106, 118, 129, 62, 38, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.V = cm3
Mathematics
1 answer:
zzz [12.3K]2 months ago
6 0
1,107 cc The scanning consists of 10 intervals: [0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15) To estimate the volume using the Midpoint Rule, n should be set to 10. Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each: [0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints: 1.5, 4.5, 7.5, 10.5, and 13.5. Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals: Cylinder 1 Midpoint=1.5, corresponding to the 2nd interval A = 18, V= height * area of the base = 18*3 = 54 cc Cylinder 2 Midpoint=4.5, corresponding to the 4th interval A = 78, V= height * area of the base = 78*3 = 234 cc Cylinder 3 Midpoint=7.5, corresponding to the 6th interval A = 106, V= height * area of the base = 106*3 = 318 cc Cylinder 4 Midpoint=10.5, corresponding to the 8th interval A = 129, V= height * area of the base = 129*3 = 387 cc Cylinder 5 Midpoint=13.5, corresponding to the 10th interval A = 38, V= height * area of the base = 38*3 = 114 cc Thus, the estimated volume is 54 + 234 + 318 + 387 + 114 = 1,107
You might be interested in
Which expressions are equivalent to RootIndex 3 StartRoot 128 EndRoot Superscript x? Select three correct answers.
AnnZ [12381]

Answer:

- 128 Superscript StartFraction 3 Over x EndFraction

- (4RootIndex 3 StartRoot 2 EndRoot)x

- (4 (2 Superscript one-third Baseline) ) Superscript x

Step-by-step explanation:

Considerando la ecuación dada (\sqrt[3]{128} )^{x}\\

De acuerdo con una de las leyes de índices,

(\sqrt[a]{m} )^{b}\\= (\sqrt{m})^\frac{b}{a}

Aplicando esta ley a la pregunta;

(\sqrt[3]{128} )^{x}\\ = {128} ^\frac{x}{3}\\ \\= (\sqrt[3]{64*2})^{x} \\ = (4\sqrt[3]{2})^{x} \\= (4(2^{1/3} )^{x} )

<pLos siguientes son ciertos de acuerdo con el cálculo presentado

128 Superscript StartFraction 3 Over x EndFraction

(4RootIndex 3 StartRoot 2 EndRoot)x

(4 (2 Superscript one-third Baseline) ) Superscript x

5 0
3 months ago
Read 2 more answers
Which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? Check all that apply.
babunello [11817]

Response: The accurate statements include:-

There are nearly equal quantities of points located above and below the x-axis.

The points are distributed haphazardly without a distinct pattern.

The total number of points matches that of the scatter plot.

Explanation:

  • A residual plot illustrates residuals on the vertical axis against the independent variable on the horizontal axis.

Consequently, the count of points is on par with the scatter plot, and roughly the same amount of points exist above and below the x-axis.

Given the random distribution of the points throughout the plot, it signifies there is no correlation, therefore, the points are scattered randomly without a clear arrangement.


8 0
2 months ago
Read 2 more answers
The function f(x)=-x^2-2x+15 is shown on the graph. What are the domain and range of the function?
PIT_PIT [12445]

Réponse:

Le domaine est l'ensemble des nombres réels

y ≤ 16

Explication étape par étape:

Le domaine est l'ensemble des valeurs x que le graphe couvre. Il n'y a aucune restriction sur les valeurs x. Le domaine est l'ensemble des nombres réels.

La plage est l'ensemble des valeurs y que le graphe couvre. Les valeurs y atteignent au maximum 16 au sommet de la parabole. Ainsi, la plage est y ≤ 16.

3 0
1 month ago
Read 2 more answers
Which lines are parallel if m4 = m5? Justify your answer.
lawyer [12517]
Angles that are opposite to each other when two lines cross are equal, therefore angle 1 is equal to angle 4. This also implies that angle 1 = angle 5. When a line crosses two parallel lines, the angles corresponding to each other are equal. So, if r and s are parallel, the angles that are formed when line l intersects line r are equal to those when l intersects line s. Thus, we have angle 1 = angle 5, angle 2 = angle 6, and so on. Hence, since angle 1 is equal to angle 5, we deduce that lines r and s are parallel.
7 0
1 month ago
In ΔHIJ, the measure of ∠J=90°, JI = 4, HJ = 3, and IH = 5. What ratio represents the tangent of ∠I?
Inessa [12570]

Answer:

The ratio  \frac{3}{4} corresponds to the tangent of ∠I.

Step-by-step explanation:

Let’s revisit the trigonometric ratios:

  • sin Ф =  \frac{opposite}{hypotenuse}
  • cos Ф =  \frac{adjacent}{hypotenuse}
  • tan Ф =  \frac{opposite}{adjacent}

For triangle HIJ

∵ m∠J = 90°

- The hypotenuse is the side opposite the right angle.

So, HI is the hypotenuse.

∵ HJ = 3 units

∵ IH = 5 units

- We’ll apply the Pythagorean Theorem to solve for HJ.

∵ (HJ)² + (IJ)² = (IH)²

∴ 3² + (IJ)² = 5²

∴ 9 + (IJ)² = 25

- Subtract 9 from both sides.

∴ (IJ)² = 16

- Taking the square root on both sides gives:

∴ IJ = 4 units

To determine the tangent of ∠I, identify the sides that are opposite and adjacent to it.

∵ HJ is opposite to ∠I

∵ IJ is adjacent to ∠I

- Utilizing the rule of tan above:

∴ tan(∠I) = \frac{HJ}{IJ}

∴ tan(∠I) = \frac{3}{4}

The ratio \frac{3}{4} indicates the tangent of ∠I.

7 0
3 months ago
Other questions:
  • Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-
    5·2 answers
  • The hourly wage increases each employee receives each year depends on the number of years of service. Every three years of servi
    7·1 answer
  • Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are
    14·2 answers
  • A greengrocer sells a melon at a profit of 37.5% on the price he pays for it. what is the ratio the cost price to the selling pr
    6·1 answer
  • Ms. Patel invested a total of $825 in two stocks. At the time of her investment, one share of Stock A was valued at $12.41 and a
    6·1 answer
  • Radio blackouts are among the most common space weather events to affect Earth. Minor radio blackouts occur, on average, twice p
    11·1 answer
  • A horticulturist conducted an experiment on 110 thirty-six inch plant boxes to see if the amount of plant food given to the plan
    11·1 answer
  • The graph shows the average shoe size for a baby or toddler as a function of age in months. What shoe size would be recommended
    15·2 answers
  • Which equation is the inverse of (x minus 4) squared minus two-thirds = 6y minus 12?
    6·2 answers
  • Give at least three examples of how earlier periods made use of the accounting process? How did the accounting process help such
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!