Need some help with some math problems

[eqlisa]

Hello,

I was hoping I could get some help with some questions that I am struggling with for a test...

1. If a number is expressed in binary, which of the following is a necessary and sufficient condition to test whether it is divisible by 2?

a. If the number does not end in 0
b. If the alternating sum of the digits is 0 or divisible by 3
c. If the number includes an even number of 1's and an even number of 0's
d. If the number, when converted to decimal form, has the sum of its digits divisible by 3



2. If A=(1, 2, 3) and B=(3, 4, 5) how many elements are in the intersection of A and B?

a. 0
b. 1
c. 3
d. 5


3. What is the sum of the 10 binomial coefficients of the form C(9, k)?

a. 45
b. 362,880
c. 512
d. 1,729


4. There are 93 students in a class; 42 like Math, while 41 like English. If 30 students don't like either subject, how many students like both?

a. 10
b. 20
c. 41
d. The answer cannot be determined from the data given


Thank you very much,
Elisabeth

 

[J77]

You need to show some attempt at answering them yourself before you get help.

 

[tacman]

Hello Elisabeth,

I would be happy to assist you with these math problems. Let's go through each question step by step:

1. To test if a number in binary is divisible by 2, the necessary and sufficient condition is that the number ends in 0. This is because in binary, all even numbers end in 0 and all odd numbers end in 1. Therefore, if a number ends in 0, it is divisible by 2, and if it ends in 1, it is not divisible by 2. So the correct answer is a. If the number does not end in 0.

2. The intersection of two sets is the set of elements that they have in common. In this case, A and B have one element in common, which is the number 3. Therefore, the correct answer is b. 1.

3. Binomial coefficients are the numbers in the expansion of a binomial expression, such as (a + b)^n. In this case, we are looking at the coefficients of the binomial expression (1 + x)^9. The sum of these coefficients is equal to 2^n, where n is the exponent. In this case, n = 9, so the sum of the coefficients is 2^9 = 512. Therefore, the correct answer is c. 512.

4. To determine the number of students who like both Math and English, we need to first subtract the number of students who don't like either subject (30) from the total number of students (93). This leaves us with 63 students who like either Math or English or both. Since 42 students like Math and 41 like English, we can subtract these numbers from 63 to find the number of students who like both. This gives us 63 - 42 - 41 = 20 students who like both Math and English. Therefore, the correct answer is b. 20.

I hope this helps you with your test preparation. If you have any further questions or need clarification, please don't hesitate to ask. Good luck on your test!