Answer:
The point C is 12.68 km away from the point A on a bearing of S23.23°W.
Step-by-step explanation:
Given that AB is 50 km and BC is 40 km as shown in the figure.
From the figure, the length of x-component of AC = |AB sin 80° - BC cos 20°|
=|50 sin 80° - 40 cos 20°|=11.65 km
The length of y-component of AC = |AB cos 80° - BC sin 20°|
=|50 cos 80° - 40 sin 20°|= 5 km
tan= 5/11.65
=23.23°
AC= km
Hence, the point C is 12.68 km away from the point A on a bearing of S23.23°W.
Answer:
<em>x² - 28x√x + 294x - 1372√x + 2404 </em>
Step-by-step explanation:
f(x) = + 3
g(x) = x - 7
h(x) = √x
f(g(h(x))) - ?
g(h(x)) = √x - 7
f(g(h(x))) = + 3 = ( √x - 7 )² × ( √x - 7 )² + 3 =
= (x - 14√x + 49)(x - 14√x + 49) + 3 =
= x² - 14x√x + 49x - 14x√x + 196x - 686√x + 49x - 686√x + 2401 + 3 =
= <em>x² - 28x√x + 294x - 1372√x + 2404</em>
Answer:
a) 14960 bottles
b) 502 bottles
Step-by-step explanation:
Given that:
Mean (μ) = 24 ounces, standard deviation (σ) = 0.14 ounces
a) From empirical rule (68−95−99.7%) , 68% of the population fall within 1 standard deviation of the mean (μ ± 1σ).
Therefore 68% fall within 0.14 ounces of the mean
the number of bottle = 22,000*68% = 14960 bottles
b) To solve this we are going to use the z score equation given as:
where x is the raw score = 23.72
From the normal probability distribution table: P(X < 23.72) = P (Z < -2) = 0.0228
The number of rejected bottles = 22000 × 0.0228 = 502 bottles