What is the sum of the first 100 positive odd numbers?

Answer:

Hence the domain is given as,b is such that b is a member of all real numbers,except b=0,a=0, a=-b

Step-by-step explanation:

The domain refers to values for which the expression is defined.

This implies that, the denominators are not equal to zero.

Hence the domain is given as,b is such that b is a member of all real numbers,except b=0,a=0, and a=-b

Answer:

Step-by-step explanation:

We are find two factors of 30 if when multiplied together will give 30 with a>b

when a = 30, b = 30/30 =1 where 30>1

The first pair of positive integers is (30, 1)

If a = 15

b = 30/15 = 2 where 15< 2

One of the factors is 2 and 15. The product of 2 and 15 is 30

Also if a = 10, b = 30/10 = 3

where 10>3

Another factor is 3 and 10. The product of 3 and 10 is also 30

If a = 6, then b = 30/6 = 5.

The two pairs of positive integers are 5 and 6 where 6>5 and the product of 6 and 5 is 30.

The different pair of positive integers (a, b) are;

(30, 1), (15, 2), (10, 3) and (6, 5)

<em>Hence there are 4 different pairs of positive integers (a,b), with greatest common factor of 1,</em>

Answer:

a) The expected number of smokers in a random sample of 140 students from this university is 16.8 smokers.

b) No, it is unlikely that smoking habits and waking up early to go to the gym on Saturday are independent.

Step-by-step explanation:

To calculate the expected numbers of smokers in a sample with size n=140 and proportion p=12%, we use the expected value of the binomial distribution:

The expected number of smokers in a random sample of 140 students from this university is 16.8 smokers.

If we take a sample at the opening of the gym, the sample is not expected to be representative of the population of the students. Most of the students that go to the gym usually have healthy habits, so the proportions of smokers is expected to be lower than the average of the university population.

Answer:

C. 0

D.2

E.4

Step-by-step explanation:

To know which numbers are solutions to the inequality, we will follow the steps below:

-3x -3 < 6

add 3 to both-side of the inequality

-3x -3 + 3 <6+3

-3x < 9

Divide both-side of the inequality by -3

-3x/-3 >9/-3

whenever we are dividing both-side of inequality by a negative number, the inequality sign will change

x > -3

all values of x that are greater than -3 will satisfy the inequality

They are 0, 2 and 4

check the solution:

for x=0

-3x -3 < 6

-3(0) -3 < 6

-3 < 6

for x = 2

-3x -3 < 6

-3(2) -3 < 6

 -6 -3 < 6

   -9< 6

for x = 4

-3x -3 < 6

-3(4)-3 < 6

-12-3 < 6

-15 < 6