Struggling with maths revision for stats diploma

[louise113]

Hello

I am starting a new course in Statistics and wanted to go over some of the basics.

I am struggling to answer the following questions -any help would be greatly appreciated!!


1. Which of the following are correct?
a) |y-3| = y+3,
b) |y-3| = y-3,
c) |y-3| = the greater of 3-y and y+3
d) |y-3| = the greater of –y+3 and -3+y
e) |y-3| = the lesser of 3-y and y+3
f) |y-3| = the lesser of –y+3 and -3+y

2. Consider the following product: 2a²´3b³. To which of the following expressions is it equivalent (there may be more than one):
a) 6a²b³
b) 5a²b³
c) 5(ab)³/a
d) 6(a²b²)²/(a²b)

3. Consider the following expression: (3a^-1)²/(6ab^-3/2)². To which of the following expressions is it equivalent:
a) (-3a)²/(-6ab^3/2)²
b) 4b^-3
c) 4b³
d) 1/(4b³)
e) b³/(4a⁴)
f) 4a^-4b^-3

4. Find the roots of each of the following equations (i.e. find the values of x for which the equality holds):
(a) 2x + 3 = 5
(b) x² - 5x + 6 = 0

5. Solve the pair of equations below
(in other words, find the point (x,y) that is common to the two lines)
y = x + 4
2y = 3x – 12


Any help would be appreciated!!!!

Thanks,

Louise

 

[ksdhart2]

1. Which of the following are correct?
a) |y-3| = y+3,
b) |y-3| = y-3,
c) |y-3| = the greater of 3-y and y+3
d) |y-3| = the greater of –y+3 and -3+y
e) |y-3| = the lesser of 3-y and y+3
f) |y-3| = the lesser of –y+3 and -3+y

A good strategy here might be to pick a random value for y, say 5, and see what happens to the absolute value expression. Does that help you form a hypothesis as to which of the statements might be correct? Now try picking another random value, say -12, and test your hypothesis. Did it hold? If it failed, can you identify why it failed? More importantly, can you identify how to fix it?

2. Consider the following product: 2a²´3b³. To which of the following expressions is it equivalent (there may be more than one):
a) 6a²b³
b) 5a²b³
c) 5(ab)³/a
d) 6(a²b²)²/(a²b)

For this problem, it may be best to return to the very basics and recall what you learned about multiplication. Note that 2a² can be written as 2 * a² and 3b³ can be written as 3 * b³. Then recall that multiplication is commutative, so you can freely put the terms in any order, without changing the expression's value. It may also be helpful to recall that b³ is the same as b * b * b.

3. Consider the following expression: (3a^-1)²/(6ab^-3/2)². To which of the following expressions is it equivalent:
a) (-3a)²/(-6ab^3/2)²
b) 4b^-3
c) 4b³
d) 1/(4b³)
e) b³/(4a⁴)
f) 4a^-4b^-3

Again, recall back to the stuff you've learned previously. This time, think about what you know about exponents. In particular, recall that (a^b)^c = a^bc.

4. Find the roots of each of the following equations (i.e. find the values of x for which the equality holds):
(a) 2x + 3 = 5
(b) x² - 5x + 6 = 0

For part (a), what if you subtracted three from both sides? Where does that lead? For part (b), recall the rules you learned about how to factor quadratics. Does the given quadratic factor nicely? What does the zero product principle mean about the roots ("solutions")?

5. Solve the pair of equations below
(in other words, find the point (x,y) that is common to the two lines)
y = x + 4
2y = 3x – 12

You're given the equations for two lines. What does it mean for two lines to intersect? Perhaps graphing the lines may prove helpful to "see" what's going on. Another way to think about it might be to note that you're given an expression, in terms of x, for y. What happens if you replace y with that expression?

If you get stuck on these problems again, that's okay. But when you reply back, please include any and all work you've done on these problems, even the parts you know for sure are wrong. Thank you.

 

[stapel]

I am struggling to answer the following questions -any help would be greatly appreciated!!

Unfortunately, since you haven't shown your work, we can't tell what, exactly, would be "helpful". I will guess that you're needing lessons over these topics.

1. Which of the following are correct?
a) |y-3| = y+3,
b) |y-3| = y-3,
c) |y-3| = the greater of 3-y and y+3
d) |y-3| = the greater of –y+3 and -3+y
e) |y-3| = the lesser of 3-y and y+3
f) |y-3| = the lesser of –y+3 and -3+y

Try here.

Note: Since the instructions ask for which of the following "are" correct, it may be that more than one option is a valid response.

2. Consider the following product: 2a²´3b³. To which of the following expressions is it equivalent (there may be more than one):
a) 6a²b³
b) 5a²b³
c) 5(ab)³/a
d) 6(a²b²)²/(a²b)

I am assuming that the accent mark after the square is a typo. Try here.

3. Consider the following expression: (3a^-1)²/(6ab^-3/2)². To which of the following expressions is it equivalent:
a) (-3a)²/(-6ab^3/2)²
b) 4b^-3
c) 4b³
d) 1/(4b³)
e) b³/(4a⁴)
f) 4a^-4b^-3

Try here and then here.

4. Find the roots of each of the following equations (i.e. find the values of x for which the equality holds):
(a) 2x + 3 = 5
(b) x² - 5x + 6 = 0

Try here for the first one. Then try here for the second one.

5. Solve the pair of equations below
(in other words, find the point (x,y) that is common to the two lines)
y = x + 4
2y = 3x – 12

Try here.

Please study at least two lessons from each link. Then please attempt the exercises. If you get stuck, you can then reply with a clear statement of your thoughts and efforts. Thank you!