Let
denote the event that a student is a freshman,
a sophomore,
a junior, and
a senior.
Let
denote the event that a student majors in engineering. By the law of total probability,
By the definition of conditional probability, we can expand each of these intersection probabilities to get
Answer:
Step-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
8.8 miles with 132 gallons of gas. You do 132 divided by 15 to get 8.8.
We know that you need 18 teaspoons of weed killer and 3 gallons of water. We can represent this as a fraction as 18/3. We can simplify this fraction. 18/3 simplified is 6/1. Next, we can multiply the numerator and denominator by 4. (6*4 is 24.) This gives us 24/4. This means that for 24 teaspoons of weed killer, we need 4 gallons of water.
