A 0.025 kg bullet enters a 2.35-kg watermelon with a speed of 217 m/s
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The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days.
That is,
Consider X be the length of the pregnancy
Mean and standard deviation of the length of the pregnancy.
Mean
Standard deviation \sigma =15
For part (a) , to find the probability of a pregnancy lasting 308 days or longer:
That is, to find
Using normal distribution,
Thus
So
Thus the probability of a pregnancy lasting 308 days or longer is given by 0.00256.
This the answer for part(a): 0.00256
For part(b), to find the length that separates premature babies from those who are not premature.
Given that the length of pregnancy is in the lowest 3%.
The z-value for the lowest of 3% is -1.8808
Then
This implies
Thus the babies who are born on or before 238 days are considered to be premature.
FIG A : ANGLE OF BAC = 67.38 °
FIG B : LENGTH OF RT = 10.549 cm
FIG C: LENGTH OF AB = 5.282 cm
FIG D: ANGLE OF ACB = 37.303°
Step-by-step explanation:
Fig A:
ABC angle = ( Opposite side) / (Hypotenuse)
Sin Ф = (12) / (13)
Ф = Sin⁻¹ ( 12/13)
Ф = 67.38 °
Fig B:
By the basic property of trigonometry
Tan Ф = (Opposite side) / (Adjacent side)
Tan Ф = (14)/ X
X= 14 / (Tan 53° )
Length of RT = 10.549 cm
Fig C:
By the basic property of trigonometry
Sin Ф = (Opposite side) / (Hypotenuse)
Sin Ф = (X) / 12.5
X = 12.5 Sin 25°
X= 5.282 cm
Fig D:
From the basic property of Trigonometry
Tan Ф = (Opposite side) / (Adjacent side)
Tan Ф = (8/10.5)
Ф = Tan⁻¹ ( 8/10.5)
Ф = 37.303°