Radius is half of the diameter so it's 7 for the diameter.
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
Step-by-step explanation:
f(4) = 4-7 = -3
g(-3) = (-3)^2 = 9
Answer:
mean=4.44
standard deviation=1.67
Step-by-step explanation:
The mean and standard deviation for the number of erroneous returns per batch can be calculated using binomial distribution. The binomial distribution is used because
i) There are one of two possible outcomes( error or no error) that can be categorized into success and failure.
ii) The experiment is repeated fix number of times 12.
iii) The probability of success remains constant at each trial i.e. 37%
iv) The trails are independent.The mean and standard deviation of binomial distribution are np and √npq
Here, n=12, p=0.37 and q=1-0.37=0.63
mean=12*0.37=4.44
standard deviation=√12*0.37*0.63=√2.8=1.67
