I'm not quite sure but the first one I'm pretty sure....
+3,+5,+7,+9 so then +11,+13,+15,+17,+19
24+11=35 => 6th term
35+13=48 => 7th term
48+15=63 => 8th term
63+17=80 => 9th term
80+19=99 => 10th term
14,34,54,74,94
Each increases by 20...
94+20= 114
114+20= 134
134+20= 154
154+20= 174
174+20= 194
37,46,55,64,73
Each increasing by 9,
73+9= 82
82+9= 91
91+9= 100
100+9= 109
109+9= 118
Answer:
standard error = 1.63
Step-by-step explanation:
To calculate the standard error we need to know the standard deviation (σ) and the sample size (n) (see the attached formula).
To obtain the standard deviation we use the given sample variance of 77.4 years:
σ²= variance
Therefore:
σ = √77.4 = 8.8
Now we can calcuate the estimated standard error:
standard error = σ /√n = 8.8/√29 = 1.63
The standard error gives us an estimation about how far the mean of the sample is from the mean of the entire population, and in this case is 1.63.
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
The shorter piece is 3/10 of the 1.5m long piece of wood.
1.5/10=0.15
0.15*3=0.45
The shorter piece is 0.45m or 45cm long.
Hope this helps :)
6>2k+4
2>2k
1>k
k has to be less than 1
Answer: a) k=0
Hope this helps:)
