Answer:
Step-by-step explanation:
Prime factorization: 43 is prime. The exponent of prime number 43 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 43 has exactly 2 factors.
Answer:
2.56 repeating
Step-by-step explanation:
Answer:
Firstly, rewrite the equation:
⅓ (18 + 27) = 81
Substitute x for the given number of it's supposed equivalent.
In this case x = 12.
⅓ (18(12) + 27) = 81
Solve using PEMDAS and simplify what is in the parenthesis first. Then, multiply.
(18 x 12) + 27 = 243
Now, solving using PEMDAS, multiply the total of what you got that was originally in the parenthesis by ⅓ .
⅓ (243) = 81
When you multiple these number they are equivalent to 81.
81 = 81
Since the equation given, when substituted x for 12, is equivalent to 81, this proves that substituting x for 12 makes this equation true.
Answer:
Step-by-step explanation:
9 - x ≤17
At some point you are going to have to turn the equation around. This would not normally be your first step, but this time it is better to start with it.
We won't do it directly. The best way to do it is to add x to both sides before you do anything else. This is not the usual way to solve these equations, but it's a good time to learn.
Inequality Rule: you must always solve for x. If it is -x then you are going to have to make an adjustment to get the x to be positive.
9 - x ≤ 17 Add x to both sides
9 - x+x ≤ 17 + x Combine
9 ≤ 17 + x Subtract 17 from both sides.
9 - 17 ≤ 17 - 17 + x
8 ≤ x
Notice that you have effectively changed the ≤ sign around, not because you have, but because the x reads differently now. It started out 9 - x ≤ 17 and when you finish solving it you get 8 is less than or equal to x. Entirely different.
Since there are two black queens out of 52 cards, there is a 2/52 chance of drawing a black queen first. This is equivalent to a 1/26 chance.
Now that we have removed a black queen, there are 51 cards left in the deck. 26 of them are red because we only took away a black card. This means that there is a 26/51 of drawing a red card next.
In order to find the probability of both of these happening, we multiply the two together. 1/26 * 26/51 = 26/1326. This reduces to 1/51. So, there is a 1/51 chance of drawing a black queen, then a red card.
