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301^4 = 8208541201 / 10000 = 820854.1201

So, it is 820,854 and 1,201/10000

The remainder is 1,201.

First, we know that segment PS is 24 units long. We will want to find QS in order to find RS. So, let's find QS

We know that PQ is half as long as QS, meaning 2 PQ = QS

We can take this as PQ + QS = PS -> PQ + 2PQ = PS -> 3PQ = PS

PS is 24 units.

3PQ=24

Divide by 3.

PQ=8

Finding PQ, we can now figure out the answer for 2PQ = QS.

2(8)=QS

16=QS

QS is 16 units long. 

In order to find RS, we need to create a similar equation as finding QS

QS= RS + QR

QR=3RS

Substitute 3RS for QR in the first equation. Substitute 16 for QS in the first equation

16 = RS + 3RS

16 = 4RS

RS = 4

So, we now know that RS is 4 units long.

Thank you! Very appreciative of the kind welcome!

Good answer!

(2+7/20)/(2/5)

First, let's make the mixed number into a fraction.

2(20)+7 = 47

Our improper fraction is 47/20.

Now, we'll divide fractions.

$\frac{47/20}{2/5}=47/20\times5/2$

Multiply the tops and bottoms separately.

47*5 = 235

20*2 = 40

The improper is 235/40

If we want to change this to a mixed number, this will take some extra steps.

First, let's simplify. 

Both numbers can be divided by 5.

235/5 = 47

40/5 = 8

Our fraction is 47/8

We can now find whole numbers from this. Dividing 47 by 8 gives us 5 with a remainder of 7.

Our mixed number is 5 and 7/8.

Hope this answer helped!

9.

Either an odd number or an even prime number.

Well, the only even prime number is 2. Everything else is divisible by 2, making it not prime.

So, we know on a 16 sided die that the numbers 1, 3, 5, 7, 9, 11, 13, and 15 are on there and apply to the odd number portion.

We have 8 numbers plus 1 extra number. 9 numbers in total, so divide 9 by 16.

9/16 = 0.5625

Rounded to the thousandths, it's 0.563.

10. 

Now, in this, we are NOT going to look at the Freshman, Sophomore, or Junior sections, as it is given that they are a Senior.

Our denominator will be 16+15+7, which is 38

Now we take however many preferred evening classes (7) and divide that by 38

7/38 = 0.1842105263157895

Rounded to the nearest thousandth, the answer is 0.184.

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!