3 1/2 - (2/3)(3 1/2) =
<span>7/2 - (2/3)(7/2) = </span>
<span>7/2 - 7/3 = </span>
<span>21/6 - 14/6 = </span>
<span>7/6 or 1 1/6 yds</span>
<h3>Answer:</h3>
1/120
<h3>Explanation:</h3>
The numerator of the probability fraction will be the number of ways to arrange 3 items: 3! = 6. So the probability fraction is ...
... 6/720 = 1/120
_____
The 3 items are the three married couples with the woman on the left.
<h3>
Answer: 24 yards, choice D</h3>
There are 4 sides to this figure (trapezoid). The left slanted side and the right most vertical side, combined with the top and bottom horizontal sides, will get us the perimeter.
left slanted side = 5 yards
right most vertical side = 4 yards (see note below)
bottom side = 9 yards
top side = 6 yards
Add up the four sides mentioned: 5+4+9+6 = 9+15 = 24
note: the rectangle has opposite sides that are the same length. While the right most side isn't labeled, it is the same length as the left side of the rectangle, so both are 4 yards long.
Another thing I should probably mention is that we do not add in the interior 4 yard side. The perimeter is only the outer or exterior sides we care about. Think of it like we're trying to fence around some property lot and we don't want to subdivide the property up. Finding the perimeter will help us find the amount of fencing needed to surround the property.
Answer:
∠F ≈ 53°
General Formulas and Concepts:
<u>Trigonometry</u>
- sin∅ = opposite over hypotenuse
- sin inverse evaluates "backward" to find the measure angle
Step-by-step explanation:
<u>Step 1: Define</u>
Looking at ∠F
opposite leg of ∠F = ED = 8
hypotenuse = FE = 10
<u>Step 2: Find m∠F</u>
- Substitute: sin∠F = 8/10
- Simplify: sin∠F = 4/5
- Take sin inverse: ∠F = sin⁻¹(4/5)
- Evaluate: ∠F = 53.1301°
- Round: ∠F ≈ 53°
the answer in standard form is 2x -5y = -3