1cm=.9m
we can multiply this by 1.2 because it will help when solving the equation
1.2cm=1.08m
this is your answer!
Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.
P(<em>X</em> ≤ 0.37) = P((<em>X</em> - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(<em>Z</em> ≤ -2)
where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)
Given the required precision for this probability, you should consult a calculator or appropriate <em>z</em>-score table. You would find that
P(<em>Z</em> ≤ -2) ≈ 0.0228
You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,
P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95
which means
P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05
The normal distribution is symmetric, so this means
P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025
which is indeed pretty close to what we found earlier.
The <em>experimental probability</em> is calculated based on the results of the experiment; since the name Ted was chosen 26 times out of 123, the experimental probability is
Typically, the <em>theoretical probability </em>assumes that events are chosen randomly; since the name Ted is one of the 6 in the hat, the theoretical probability is
If we <em>increased</em> the number of names in the hat, we would expect both the experimental and theoretical probability to decrease, since there are now more names to choose from. Similarly, if we <em>decreased</em> the number of names in the hat, the experimental and theoretical probability would increase.
Answer:
Step-by-step explanation:
1). In ΔABC,
For angle A as a reference angle,
Opposite side of ∠A → BC
Adjacent side of ∠A → AC
Hypotenuse → AB
2). By using tangent ratio in ΔYWZ,
tan(72°) =
tan(72°) =
x =
x = 3.899
x ≈ 3.9
3). By using sine rule in ΔKNM,
tan(x°) =
tan(x) =
x =
x = 19.03
x ≈ 19.0°
4). By applying cosine ratio in ΔJKF,
tan(70°) =
tan(70) =
x =
x = 21.838
x ≈ 21.8
It states that a(b + c) = ab + ac