(3 x 10) x 8 = 3 x (10 x 8)
this is called the associative property of multiplication.
it states : (a * b) * c = a * (b * c)
Answer:
Step-by-step explanation:
Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...
5(s+4) = (s+32)+4
5s +20 = s +36 . . . . . eliminate parentheses
4s = 16 . . . . . . . . . . . . subtract s+20
s = 4
The son is now 4 years old; the father, 36.
_____
<em>Alternate solution</em>
In 4 years, the ratio of ages is ...
father : son = 5 : 1
The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...
father : son = 40 : 8
So, now (4 years earlier), the ages must be ...
father: 36; son: 4.
Data:
l and m are parallel lines
QR and ST are perpendicular in R
Angle 1 is 63°
The angle formed by perpendicular lines is a right angle (90°)
Angles 1 and 3 are alternate angles: angles that occur on opposite sides of a transversal line that is crossing two parallel.
Alternate angles are congruent, have the same measure.

The sum of the interior angles of a triangle is always 180°. In triangle QRT:

Use the equation above to find the measure of angle 2:

Then, the measure of angle 2 is 27°
60% decrease.
$105-$42 = $63
$63/$105 = 0.6
0.6 x 100 = 60
Answer:
The probability that a student is an undergraduate student, given that the student received a plus grade is 0.92
Step-by-step explanation:
The conditional probability of an event <em>B</em> given that another event <em>A</em> has already occurred is:

Denote the events as follows:
<em>X</em> = a students is a graduate
<em>Y </em>= a students is a under-graduate
+ = a student received one or more plus grades
- = a student received one or more minus grades
Consider the tree diagram below.
According to the tree diagram, the probability that a student is an undergraduate student, given that the student received a plus grade is:
P (+ | Y) = 0.92
Thus, the probability that a student is an undergraduate student, given that the student received a plus grade is 0.92.