Rate at which risk of down syndrome is changing is approximated by function r(x) = 0.004641x2 − 0.3012x + 4.9 (20 ≤ x ≤ 45) wher
e r(x) measured in percentage of births per year and x is maternal age at delivery. find function f giving risk as percentage of births when maternal age at delivery is x years, given that risk of down syndrome at 30 is 0.14% of births.
1 answer:
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Answer:
" Vertical angles are equal " ⇒ 2nd answer
Step-by-step explanation:
* Refer to the attached illustration
- Three lines intersect at point D.
- We have to identify the missing justification in step 3.
∵ Line FA intersects line EC at point D.
- When two lines cross, the angles created are referred to as
vertical angles.
- By the vertical angles theorem, vertical angles are equal.
Thus, ∠ADC and ∠FDE are vertical angles.
Since vertical angles are equal
∴ ∠EDF ≅ ∠ADC
Thus, m∠EDF ≅ m∠ADC
Given that m∠EDF = 120°.
∵ m∠ADC is the sum of m∠ADB and m∠BDC.
Therefore, m∠ADB + m∠BDC = 120°.
∵ m∠ADB = (3x)° ⇒ given.
∵ m∠BDC = (2x)° ⇒ given.
Thus, 3x + 2x = 120 ⇒ combine like terms.
Thus, 5x = 120 ⇒ divide both sides by 5.
Thus, x = 24.
Column (1) Column (2)
m∠EDF = 120° given
m∠ADB = 3 x given
m∠BDC = 2 x given
∠EDF and ∠ADC are vertical angles definition of vertical angles
∠EDF is equal to ∠ADC vertical angles are equal
equal
m∠ADC = m∠ADB + m∠BDC angle addition principle.
m∠EDF = m∠ADC definition of equality.
m∠EDF = m∠ADB + m∠BDC substitution.
120° = 3 x + 2 x substitution.
120 = 5 x addition.
x = 24 division.
∴ The missing justification is " vertical angles are equal "
- From the reasoning above, ∠ADC and ∠FDE are vertical angles and therefore they are equal according to the vertical angle theorem.
Answer:
Step-by-step explanation:
It has been established that the count of drivers traveling between a specific origin and destination in a certain time frame follows a Poisson distribution with a mean μ = 20 (as indicated in the article "Dynamic Ride Sharing: Theory and Practice"†).
a)
b)
c)
d) 2 standard deviations = 2(20) = 40
Thus, this means the range for 2 standard deviations is
20-40, 20+40
which equates to (0,60)