Answer:
2/5 are girls so 40
Step-by-step explanation:
100 divided by 5 is 20.
BOYS: 20 x 3= 60
GIRLS: 20 x 2= 40
60+40=100
Hope this helps (:
Answer: quantitative
Step-by-step explanation:
Measured variables in statistics may be subdivided into quantitative or Qualitative variables depending on whether the variable in question is numeric or non-numeric. Variables which are designed to evaluate on the basis of Number or quantity may be termed as quantitative variables while those which measure attribute and are used for characterization are called Qualitative variables. In the scenario above, the variable is concerned with the determination of concentration of nitrogen draining into water bodies, concentration follows that numeric calculations be Made in other to determine the amount of nitrogen in milligram per Litre in a particular water body in other to prevent its effect on wildlife which could result from excessive concentration in water bodies.
Answer:
The required rectangular form of the given complex polar form :
z1 = -3√2 - 3√2i
Step-by-step explanation:
![z_1=6[\cos (\frac{5\pi}{4}) + i\sin(\frac{5\pi}{4})]...........(1)\\\\Now,\cos (\frac{5\pi}{4})=\cos(\pi+\frac{\pi}{4})\\\\=-\cos(\frac{\pi}{4})\\\\=-\frac{1}{\sqrt{2}}\\\\And,\sin (\frac{5\pi}{4})=\sin(\pi+\frac{\pi}{4})\\\\=-\sin(\frac{\pi}{4})\\\\=-\frac{1}{\sqrt{2}}](https://tex.z-dn.net/?f=z_1%3D6%5B%5Ccos%20%28%5Cfrac%7B5%5Cpi%7D%7B4%7D%29%20%2B%20i%5Csin%28%5Cfrac%7B5%5Cpi%7D%7B4%7D%29%5D...........%281%29%5C%5C%5C%5CNow%2C%5Ccos%20%28%5Cfrac%7B5%5Cpi%7D%7B4%7D%29%3D%5Ccos%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C%5C%5C%3D-%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C%5C%5C%3D-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5C%5C%5C%5CAnd%2C%5Csin%20%28%5Cfrac%7B5%5Cpi%7D%7B4%7D%29%3D%5Csin%28%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C%5C%5C%3D-%5Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5C%5C%5C%5C%3D-%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D)
On substituting the obtained values in equation (1)
![z_1=6[\frac{-1}{\sqrt{2}}-i\cdot \frac{1}{\sqrt{2}}]\\\\\implies z_1=-3\sqrt{2}- 3\sqrt{2}\cdot i](https://tex.z-dn.net/?f=z_1%3D6%5B%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D-i%5Ccdot%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5D%5C%5C%5C%5C%5Cimplies%20z_1%3D-3%5Csqrt%7B2%7D-%203%5Csqrt%7B2%7D%5Ccdot%20i)
Hence, the required rectangular form of the given complex polar form :
z1 = -3√2 - 3√2i
Answer:
see explanation
Step-by-step explanation:
Using the cosine and tangent ratios in the right triangle
cos41° =
=
= 
Multiply both sides by VX
VX × cos41° = 7 ( divide both sides by cos41° )
VX =
≈ 9.3
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tan41° =
=
= 
Multiply both sides by 7
7 × tan41° = WX, thus
WX ≈ 6.1
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The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180° for ∠ X
∠ X = 180° - (90 + 41)° = 180° - 131° = 49°