Answer:
Step-by-step explanation:
<h3><u>Question 6</u></h3>
To find the greatest common factor (GCF), first list the prime factors of each number:
- 42 = 2 × 3 × 7
- 60 = 2 × 2 × 3 × 5
42 and 60 share one 2 and one 3 in common.
Multiply them together to get the GCF: 2 × 3 = 6.
Therefore, 6 is the GCF of 42 and 60.
Divide the numerator and the denominator by the found GCF:
<h3><u>Question 7</u></h3>
To find the greatest common factor (GCF), first list the prime factors of each number:
- 80 = 2 × 2 × 2 × 2 × 5
- 272 = 2 × 2 × 2 × 2 × 17
80 and 272 share four 2s in common.
Multiply them together to get the GCF: 2 × 2 × 2 × 2 = 16.
Therefore, 16 is the GCF of 80 and 272.
Divide the numerator and the denominator by the found GCF:
Yes, your answer is correct.
Answer: x= -6; y= -1
Step-by-step explanation:
-4x + y = 23
4x - 9y = - 15
-4x + y = 23
y = 23 + 4x [Add 4x to both side]
4x - 9(23 + 4x) = - 15
4x - 207 - 36x = - 15
-32x - 207 = -15
-32x = 192 [Add 207 to both side]
x = -6 [Divide -32 from both side]
-4x + y = 23
-4(-6) + y = 23 [Plug in -6 for x]
24 + y = 23 [Subtract 24 from both side]
y = -1
Looks like a badly encoded/decoded symbol. It's supposed to be a minus sign, so you're asked to find the expectation of 2<em>X </em>² - <em>Y</em>.
If you don't know how <em>X</em> or <em>Y</em> are distributed, but you know E[<em>X</em> ²] and E[<em>Y</em>], then it's as simple as distributing the expectation over the sum:
E[2<em>X </em>² - <em>Y</em>] = 2 E[<em>X </em>²] - E[<em>Y</em>]
Or, if you're given the expectation and variance of <em>X</em>, you have
Var[<em>X</em>] = E[<em>X</em> ²] - E[<em>X</em>]²
→ E[2<em>X </em>² - <em>Y</em>] = 2 (Var[<em>X</em>] + E[<em>X</em>]²) - E[<em>Y</em>]
Otherwise, you may be given the density function, or joint density, in which case you can determine the expectations by computing an integral or sum.
