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The answer is 27

I don't understand the step \(0.99\cdot 100-0.98(100-x)=x\), why do you do this? Can you explain more? Thanks.

the answer is 3 because if you change the addition sign to a subtraction sign (because a positive and a negative equal a positive) you're just subtracting :)

Circumference = Diameter x Pi
2.5 feet x 12 inches =30 inches - the radius of the front wheel.
30 x 2 =60 inches - the diameter of the front wheel.
C=60 x Pi =60Pi - inches - the circumference of the front wheel.

4 x 2 =8 inches - the diameter of the back wheel.
C =8 x Pi =8Pi - inches - the circumference of the back wheel.
100 x [60Pi / 8Pi] =6,000Pi / 8Pi =750 revolutions the back wheel will make for 100 revolutions of the front wheel.

I encourage you to utilize the reference problems that you have been given already to tackle this problem. Below is the link to those reference problems:

Substitute in the given value for x and y into the given expression and evaluate.

\(-3x+6y; x=-3, y=6\\ -3*-3+6*6\\ 9+36\\ 45\)

This is quite simple to simplify.

\(-4 < x-2 < \hspace{1mm} 3 \\ +2 \hspace{8mm} + 2 \hspace{1mm} +2 \\ \overline{\quad\quad\quad\quad\quad\quad\quad}\\ -2 < x < \hspace{8mm} 5\)

When this inequality is represented via a number line graph, it looks like this:
 

Order of operations is a strict set of rules that dictate how to evaluate any expression. I have laid the order of operations out for you:
 

1. Simplify within grouping symbols such as parentheses or brackets from left to right.

2. Simplify exponents from left to right.

3. Perform multiplication or division, whichever operation comes first from left to right.

4. Perform addition or subtraction, whichever operation comes first from left to right.

If something is higher on the list, then it has greater priority. Let's apply this knowledge to this particular problem:

Gary hit two targets, and each target awarded Gary 70 points. \(2*70\) is one way to represent the total points Gary scored. However, he lost 145 points for taking too long. \(-145\) is one way to represent this change of points. 

\(2*70-145=140-145=-5\)

Hi, tertre!

\(-1^2=-1\).

This confuses most people, and this is a quite common error. I would like to correct it once and for all!

\(-1^2=-(1^2)=-(1*1)=-1\\ (-1)^2=-1*-1=1\)

Do you see the difference? The order of operations is strict.

0 is the answer

\((1+\sqrt{3})-(1-\sqrt{3}) = 1-1 + \sqrt{3}+\sqrt{3}=0+2\sqrt{3}\)

First, expand \(2(3- \sqrt3)\) to \(6-2\sqrt3\) , by applying the distributive property, ab-ac.

Next, we expand the second term, \(-3(1- \sqrt3)\) to \(-3+3\sqrt{3}\) , by again using the distributive property.

Finally, we simplify, (by adding similar elements), \(6-2\sqrt{3}-3+3\sqrt{3}\) and that will get us \(\boxed{3+\sqrt{3}}.\)

All that is necessary is some simplifying. That's all.

Check: $200, also she made two deposits of $80, so \(200+2(80)=200+160=\boxed{360}\) 

\(-2+4=2.\)

\(-1^2=-1*-1=\boxed{1}\).

Negative changes to positive, so \(3-(-9)=3+9=\boxed{12}\) .

\(3-(-9)=3+9=12\)

\(-12+5=-7\)

\(-5+3=-2\)

thanks <3

Thank you very much :)

There's only 1 zero of f(x) in the interval [-2,4]

1 point can't enclose anything....

let's first figure out how many permutations do have the 3rd term equal to 3

The first number we have 4 choices (not 1 or 3), the second number we have 4 choices, the 3rd number is 3, the 4th there are 3 choices, 5th 2 choices.

This is 4 x 4! = 96

The total number of permutations in S is just 5 x 5! = 600 (do you see why?)

and thus

P[term 3 = 3] = 96/600 = 4/25