The answer would be Addition property of equality i belive
Answer:
Test statistic = - 3.354
We reject H0 and conclude that the growth rate of the new shrub is less than 3cm per week.
Step-by-step explanation:
H0 : μ = 3
H1 : μ < 3
The test statistic = (xbar - μ) / (s/ √n)
Xbar = 1.50
μ = 3
s = 3
n = 45
Test statistic = (1.5 - 3) / (3/ √45)
Test statistic = - 1.5 / 0.4472135
Test statistic = - 3.354
Pvalue, using the Pvalue from Z score calculator :
Pvalue = 0.00039826
α = 0.05
Pvalue < α ; We reject H0 and conclude that the growth rate of the new shrub is less than 3cm per week.
Answer:
The decimal of 17/6=2.8333333333
Using <span>De Moivre's formula
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if z = a ( cos x + i sin x ) ⇒⇒⇒ ∴ z^n = a^n ( cos nx + i sin nx)
Part (1)
∴ [ 3 (cos 27° + i sin 27°) ]⁵ = (3⁵) ( cos 5*27° + i sin 5*27°)
= 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
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Part (2)
The angle 135° in the second quadrant ⇒ sin is (+) and cos is (-)
and its reference angle = 180° - 135° = 45°
sin 45° = cos 45°= 1/√2 = (√2)/2
∴ sin 135° = (√2)/2 and cos 135° = -(√2)/2
∴ 243 ( cos 135° + i sin 135°) = 243 [ -(√2)/2 + i (√2)/2 ]
= - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
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The correct answers are options (1) and (3)
option (1) ⇒⇒⇒ 243 ( cos 135° + i sin 135°) ⇒⇒⇒⇒ Polar form
option (3) ⇒⇒⇒ - 243(√2)/2 + 243 (√2)/2 i ⇒⇒⇒⇒ standard form
