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33/60 reduces to 11/20

\({33 \over{60}} = {11 \over{20}}\) This is because 33 AND 60 can be divided by 3, which gives us 11 and 20

1.

For this, you'll use factorials. 

So, to find the possible orders, you have to do 6!. This is the same as 6*5*4*3*2*1.

6! = 720

So, the answer is 720.

2. 

You can actually do this on the calculator as well! Use nPr(n, r). n is the number on the left side, and r is on the right.

nPr(9, 5) = 15,120

So your answer is 15,120.

Hope this helped!

First, let's find the remaining money. 

164-147.5

164-147.5 = 16.5

So, he has $16.50 left.

Now, we take 16.5 and divide it by 2.79. This will give the amount of milk he can buy

16.5/2.79 = 5.9139784946236559

Well, we can't buy a part of a milk jug, so we have to round DOWN since we can't just get milk for free as well. 

So, Lucas can buy 5 gallons of milk with a remaining amount of $2.55. Maybe buy some candy for all the hard work he's gonna be doing? 

\(y = {-7 \pm \sqrt{7^2-4(1)(-6)} \over 2}\)

Convenient that the first thing from the LaTeX button is the quadratic formula. (Before this, subtract 6 from both sides. It's now y²+7y-6=0)

Evaluate what is under the root.

-4*-6=24

7²=49

49+24=73

We now have \(y= {-7 \pm \sqrt{73} \over 2}\)

Nothing past this can be done. Your answer is A .

Whoops! Might have! Thank you for the correction!

For this, we'll be using the trig. function tangent. 

Tangent is the opposite over the adjacent (TOA)

x=15*tan(70) = x=18.329

The antenna is 18' to the nearest foot. (Rounding 18.3 to the nearest foot brings us to 18)

EDIT: My answer is incorrect, at least if it's in degrees (which it is).

The correct answer is 41'. 

Definitely shows the importance of changing the mode!

10.

Given that the person is a junior is important here. We are ONLY looking at the category of "Junior"

There's a total of 28 juniors surveyed, so the denominator is 28

13/28 = 0.4642857142857143

Rounded to the nearest thousandth, the answer is 0.464 .

11. 

We're looking at 24% of 74%.

(Seems confusing)

Multiply the percents.

0.24*0.74 = 0.1776

Rounded to the thousandth, that's 0.178

Turn it into a percentage, it's 17.8%

Final answer: 17.8%

The "!" in math means that it's factorial.

For example, 7! is the same as 7*6*5*4*3*2*1, which equals 5040.

EDIT: Included Question 2

Question 1: Simplify the expression: \((2-3i)(4+2i)\)

For this, we'll use the FOIL method.

2*4=8

8+__+__+__

2*2i=4i

8+4i+__+__

-3i*4=-12i

8+4i-12i+__

-3i*2i=-6i²

(I'm assuming i=sqrt(-1))

8+4i-12i+6=14-8i

Option S is your answer

Question 2: Simplify the expression: \((3x^4+9x^3-7x+15)+(-6x^4-8x^2+5x-3)\)

This is adding like terms.

First, let's start with x^4

3-6=-3

-3x⁴+9x³-8x²+__+__

There were only one x^3 and x^2 in the expression, so we know that part for sure.

Now, to the x term.

-7+5=-2

-3x⁴+9x³-8x²-2x+__

Now, to the normal numbers.

15-3=12

Final answer: -3x⁴+9x³-8x²-2x+12

Hope this helped!