<u>Answer</u>
8√2
<u>Explanation</u>
Simply: 4√2 + 7√2 - 3√2
Let √2 = x
4√2 + 7√2 - 3√2 = 4x + 7x - 3x
= 11x - 3x
= 8x
Substituting x with √2
4√2 + 7√2 - 3√2 = 8√2
Answer:
We accept H₀ , we do not have enought evidence for rejecting H₀
Step-by-step explanation:
Normal Distribution
sample size n = 60
standard deviation σ = 15
1.Hypothesis Test : Is a one tailed-test on the right
H₀ null hypothesis μ₀ = 50
Hₐ alternative hypothesis μ₀ > 50
2.-We will do the test for a significance level α = 0,01 tht means for a 99% interval of confidence
then z(c) = 2.32
3.- We compute z(s)
z(s) = [ ( μ - μ₀ ) /( σ/√n ) ⇒ z(s) = ( 2 * √60 ) / 15
z(s) = 15.49/15 ⇒ z(s) = 1.033
4.- We compare values of z(c) and z(s)
z(s) < z(c) 1.033 < 2.32
z(s) is in the acceptance region so we accept H₀ , we do not have enough evidence for rejecting H₀
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)!!!
