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Vilka [71]
3 years ago
7

The following shows the correlation between the length of a persons handspan and how many jolly ranchers they can pick up with o

ne hand. Which of the following correlation coefficients is closest to the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? PLEASE HELPPP!!!

Mathematics
1 answer:
9966 [12]3 years ago
3 0
The best choice from the ones viewable in your picture is B) 1.

With that being said, 1 is used to indicate a perfect fit, which there is not one for this plot.
However, 0 would not be correct either, as 0 implies no correlation.  We can see from the graph that there is a correlation.

-0.95 would not work either, as the line appears to trend upward; a negative correlation coefficient indicates it trends down.
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49 - 9 / 8

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What is the approximate solution to this equation? 15(3)^2x=90
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x ≈ 0.67

Step-by-step explanation:

15(3)^2x = 90\\\\15(9)x = 90\\\\135x = 90\\\\x = 90/135\\\\ x = 2/3\\\\x = 0.666...\\\\x = 0.67 \ (rounded \ to \ nearest \ hundredth )

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2 years ago
The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t
nirvana33 [79]

Answer:

\frac{dr}{dt}  = -1.325 \ cm/s

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Calculus</u>

Derivatives

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

<u>Step 1: Define</u>

Given:

<u />V = \frac{4}{3} \pi r^3<u />

<u />\frac{dV}{dt} = -116 \ cm^3/s<u />

<u />V = 77 \ cm^3<u />

<u />

<u>Step 2: Solve for </u><em><u>r</u></em>

  1. Substitute:                    77 = \frac{4}{3} \pi r^3
  2. Isolate <em>r</em> term:               \frac{77}{\frac{4}{3} \pi} = r^3
  3. Isolate <em>r</em>:                        \sqrt[3]{\frac{77}{\frac{4}{3} \pi}}  = r
  4. Evaluate:                       2.63917  = r
  5. Rewrite:                         r = 2.63917 \ cm

<u>Step 3: Differentiate</u>

<em>Differentiate the Volume Formula with respect to time t.</em>

  1. Define:                                                                                                            V = \frac{4}{3} \pi r^3
  2. Differentiate [Basic Power Rule]:                                                                   \frac{dV}{dt}  = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}
  3. Simplify:                                                                                                           \frac{dV}{dt}  = 4 \pi r^2 \cdot \frac{dr}{dt}

<u>Step 4: Find radius rate</u>

  1. Substitute in variables:                    -116 \ cm^3/sec  = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}
  2. Isolate dr/dt rate:                             \frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}
  3. Evaluate:                                          -1.3253 \ cm/s = \frac{dr}{dt}
  4. Rewrite:                                           \frac{dr}{dt}  = -1.3253 \ cm/s
  5. Round:                                             \frac{dr}{dt}  = -1.325 \ cm/s

Our radius is decreasing at a rate of -1.325 cm per second.

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4 years ago
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