~~~~WARNING HARD MATH~~~~
An integer from 100 to 999, inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit?
Multiple Choice:
Underline or circle the letter that best solves the question.
a) 19/900
b)81/900
c)90/900
d)171/900
e)271/1,000
For all real numbers b and c such that the product of and 3 is b, write an following expression that represents the sum of c and 3 in terms of b.
Expression:
__________________________________________
What is the square root of 65,536?
Multiple Choice:
Underline of circle the letter that best solves the question.
a) 725
b) 265
c) 276
d) 256
e) 267
COMING SOON! BE SURE TO WATCH OUT FOR MORE SHORT QUIZZES AND TESTS >3<
Well, well, well. Looks like we've got some math questions here. Let's see if my funny bone can help us solve these!
Question 1: What is the probability that a randomly chosen number between 100 and 999 will have 0 as at least 1 digit?
Well, let's break it down. First, we need to find out how many numbers in that range have at least one 0 as a digit. We can split it into three cases - numbers with 0 in the hundreds place, numbers with 0 in the tens place, and numbers with 0 in the units place.
We have 10 choices for the hundreds place (0-9), and after choosing that, we have 9 choices for the tens place (0-9, except for the one we've already chosen), and finally 9 choices for the units place. So, we have 10 * 9 * 9 = 810 possibilities with at least one 0 as a digit.
Now, let's find the probability. The total number of possibilities is 999 - 100 + 1 = 900 (don't forget to include both endpoints). So, the probability is 810/900 = 9/10.
Hmmm, none of the given options match exactly. But the closest one is 81/900 (b), so let's go with that. Though, it's not quite right. Guess we'll have to keep our clown noses on for the rest of the quizzing!
Question 2: For all real numbers b and c such that the product of b and 3 is b, what is the sum of c and 3 in terms of b?
So, the product of b and 3 is b... Are we sure we didn't mess up here? It looks like we have a special number called 0. This is a tricky one, because any number multiplied by 0 is always 0. Therefore, c must be 0, which means the sum of c and 3 is just 3!
On to the final question!
Question 3: What is the square root of 65,536?
Well, 65,536, eh? That's a pretty big number. But don't worry, I'll simplify it for you. The square root of 65,536 is indeed 256 (d)!
Phew! That was some math workout. I hope my clowning around helped you out. Keep an eye out for more quizzes and tests, and remember to smile even in the face of difficult math problems!
To find the probability that the number chosen will have 0 as at least 1 digit, we need to find the total number of possible outcomes (numbers from 100 to 999) and the number of favorable outcomes (numbers with at least one 0 digit).
Total number of possible outcomes: There are 900 numbers from 100 to 999 (inclusive).
Number of favorable outcomes: There are several ways to approach this.
One way is to find the complement of the event (numbers with no 0 digit) and subtract it from the total number of outcomes.
Numbers with no 0 digit: We exclude the possibility of choosing 0 as the hundreds place and then multiply it by the possibilities for the tens place (1-9) and units place (1-9). So, there are 9 choices for the hundreds place and 9 choices for each of the tens and units places, giving us 9 * 9 * 9 = 729 numbers without a 0 digit.
Favorable outcomes: Subtracting the numbers with no 0 digit from the total number of outcomes, we get: 900 - 729 = 171.
Therefore, the probability of choosing a number with at least one 0 digit is 171/900.
For the first multiple-choice question, the correct answer is d) 171/900.
To write an expression that represents the sum of c and 3 in terms of b, we can use the given information that the product of b and 3 is equal to b * 3.
Expression: c + 3
Therefore, the sum of c and 3 in terms of b is c + 3.
For the second multiple-choice question, to find the square root of 65,536, we can take the square root of both sides of the equation as the square root operation is the inverse of the square operation.
√(65,536) = √(256 * 256) = 256
Therefore, the square root of 65,536 is 256.
For the second multiple-choice question, the correct answer is d) 256.