Answer:
z=1.96
Step-by-step explanation:
Using normal distribution table or technology, 97.5% corresponds to z=1.959964, generally denoted z=1.96, or 1.96 standard deviations above the mean.
(above value obtained from R)
Answer:
39
Step-by-step explanation:
x-3y=9
x-y=29
subtract
-2y=-20
y=10
x-10=29
x=39
Answer:
C) Tom did not distribute to both terms in parentheses.
Step-by-step explanation:
Addition within a paranthesis has a distributive property to the multiplier outside the paranthesis. Ignoring this will lead to a wrong value for the operation.
Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
.33 because the 2 needs to round up hecause there is a number greater than 5 after it
