<span>With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.</span>
Answer:
A) The theoretical probability of choosing a heart is 1/16 greater than the experimental probability of choosing a hear
Step-by-step explanation:
By the binomial theorem,

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.
Answer:
The graphs are missing, but we can find the inequality for this problem:
She has $60.
The price of a T-shirt is $10, the price of a sweatshirt is $14.
If T is the number of T-shirts she buys, and S is the number of sweatshirts that she buys, we have:
T + S ≥ 5 (because she wants to buy at least 5 items)
T*$10 + S*$14 < $60 (because she wants to spend under $60)
Those two inequalities define the number of T-shirts and sweatshirts that she can buy.
Let’s look at the permutations of the letters “ABC.” We can write the letters in any of the following ways:
ABC
ACB
BAC
BCA
CBA
CAB
Since there are 3 choices for the first spot, two for the next and 1 for the last we end up with (3)(2)(1) = 6 permutations. Using the symbolism of permutations we have:

. Note that the first 3 should also be small and low like the second one but I couldn’t get that to look right.
Now let’s see how this changes if the letters are AAB. Since the two As are identical, we end up with fewer permutations.
AAB
ABA
BAA
To make the point a bit better let’s think of one A are regular and one as bold
A.
ABA and AB
A look different now because we used bold for one of the As but if we don’t do this we see that these are actual the same. If they represented a word they would be the same exact word.
So in this case the formula would be

. We use 2! In the denominator because there are 2 repeating letters. If there were three we would use 3!
Hopefully, this is enough to let you see that the answer is A. The number of permutations is limited by the number of items that are identical.