Answer:
3
Step-by-step explanation:
1926/9=214
1923+3=1926
Answer:
Hi! The formula for surface area is:
area = 2lw + 2lh + 2hw
(l = length, w = width, h = height.)
<em>Hope this helps! :)</em>
y = x^2 + 2x...eqn 1
y = 3x + 20...eqn 2
subst for y in eqn 1...
=> x^2 +2x = 3x +20
=> x^2 - x - 20 =0
=> (x-5) (x+4) =0
=> x = 5 or -4
for x =5, y = 35 (sub for x in eqn 1 or 2)
for x = -4, y = 8 (sub for x in eqn 1 or 2)
We can solve this problem by referring to the standard
probability distribution tables for z.
We are required to find for the number of samples given the
proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value
of z equivalent to:
z = 1.96
Since the problem states that it should be within the true
proportion then p = 0.5
Now we can find for the sample size using the formula:
n = (z^2) p q /E^2
where,
<span> p = 0.5</span>
q = 1 – p = 0.5
E = estimate of 5% = 0.05
Substituting:
n = (1.96^2) 0.5 * 0.5 / 0.05^2
n = 384.16
<span>Around 385students are required.</span>
Answer:
See Below.
Step-by-step explanation:
We want to show that the function:
Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:
Simplify:
Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
