Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches.two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 3 inches.

Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Show all work.

Answers

Answer 1

Answer: Let r represent the radius of the smaller circle and R the radius of the larger circle.
Apply ratios: the radius of smaller circle to radius of larger circle, i.e.

r: R = 3 : 7.

I complete rotation = 360 degrees.

Part 1:

For one complete rotation of the smaller circle, the larger circle is rotated through: (3/7)*(360) = 154.3 degrees

Part 2:
For one complete rotation of the larger circle, the larger circle is rotated through: (7/3)*(360) = 840.0 degrees

This is equivalent to (840/360) = 2.3 rotations

Alternatively, use the ratios:
The number of rotations = R/r = 7/3 = 2.3 rotations

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The box plots below show the lifespan, in months, of laptop batteries manufactured by four companies:Based on the data, which company's batteries have the highest median lifespan?

Company A
Company B
Company C
Company D

Answers

I studied the image of the box plot that should have been part of this problem.

Company Median
A 23
B 24
C 22
D 22.5

Company B has batteries that have the highest median lifespan of 24 months.

Answer:

company B

Step-by-step explanation:

Round 4745 to the nearest thousand

Answers

Answer:

5000

Step-by-step explanation:

4745 is closer to 5000 than 4000 because it's over 4500

A circle is inscribed in an equilateral triangle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded. A. About 25%
B. About 40%
C. About 60%
D. About 50%

Answers

If $r$ is the radius of the circle, then the side length of the triangle is $2r\sqrt3$ .

The area of the circle is $\pi r^2$ , while the area of the triangle is $3r^2\sqrt3$ .

So, the probability of selecting a random point in the white space is

$1-(\pi r^2)/(3r^2\sqrt3)=1-(\pi)/(3\sqrt3)\approx0.395\approx40\%$

Answer:

about 60%

Step-by-step explanation:

just took the test

The 7 in 7000 is how many times greater than the 7 in 70?

Answers

Each 0 I believe is worth 10 times so 7000 is 30 times more greater.

1. Write an equation in point slope form for the line that has a slope of 6 and contains the point (-8,-7).2. The points (-4,-3) and (-1,-8) are on a line. Find the intercepts to the nearest tenth.

3. Solve 2x-3y=11 by elimination. Express your answer as an ordered paired.
3x+3y=9

4. Solve 2x - 5y = -7 by elimination. Express your answer as an ordered pair.
5x - 3y = 11

5. Order the list of numbers from least to greatest
4.9 X 10^11 , 8.9 X 10 ^18 , 1.3 X 10 ^8 , 6.7 X 10 ^8 , 2.7 X 10 ^18

Answers

1. y - y₁ = m(x - x₁)
     y - (-7) = 6(x - (-8))
       y + 7 = 6(x + 8)
   y + 7 = 6(x) + 6(8)
   y + 7 = 6x + 48
      - 7 -   7
   y = 6x + 41

2. y₂ - y₁ = -8 - (-3) = -8 + 3 = -5 = -1²/₃
    x₂ - x₁ -1 - (-4) -1 + 4 3

3. 2x - 3y = 11
    3x + 3y =   9
      5x = 20
   5 5
      x = 4
     2x - 3y = 11
   2(4) - 3y = 11
   8 - 3y = 11
   - 8 - 8
   -3y = 3
      -3    -3
      y = -1
      (x, y) = (4, -1)

4. 2x - 5y = -7 ⇒   -6x + 15y = 21
    5x - 3y = 11 ⇒ -25x + 15y = -55
      19x = 76
   19    19
      x = 4
   2x - 5y = -7
   2(4) - 5y = -7
   8 - 5y = -7
   - 8 - 8
   -5y = -15
      -5 -5
      y = 3
      (x, y) = (4, 3)

5. 4.9 × 10¹¹, 8.9 × 10¹⁸, 1.3 × 10⁸, 6.7 × 10⁸, 2.7 × 10⁸
    1.3 × 10³, 2.7 × 10⁸, 6.7 × 10⁸, 4.9 × 10¹¹, 8.9 × 10¹⁸
    Least        Greatest

Solve the following system of equations by graphing and select the correct answer below:2x + 6y = 20
3x _ 2y = 8

Answers:
x = 4, y = 2
x = 4, y = _2
x = _2, y = 4
x = 2, y = 4