A ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s. The radius of the ride is 9.0 meters. Which of th
e following shows the direction of the acceleration of the riders?
a
b
c
d
a
b
c
d
1 answer:
Answer with explanation:
It is given that , ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s.
Radius of Circle = 9.0 meters
Acceleration is rate of change of velocity,which will be perpendicular to radius vector.
Also, in terms of mathematics, line from center that is radius , to point of contact that is tangent line ,which is on the circle are perpendicular to each another.
→r(radius vector) ⊥ a(Acceleration vector).
So, In option A, Radius vector is Perpendicular to acceleration of riders.
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Answer:
a)0,45119
b)1
Step-by-step explanation:
For part A of the problem we must first find the probability that both people in the couple have the same birthday (April 30)
Now the poisson approximation is used
λ=nP=80000*1/133225=0,6
Now, let X be the number of couples that birth April 30
P(X ≥ 1) =
1 − P(X = 0) =
P(X ≥ 1) = 0,45119
B) Now want to find the
probability that both partners celebrated their birthday on th, assuming that the year is 52 weeks and therefore 52 thursday
Now the poisson approximation is used
λ=nP=80000*52/133225=31.225
Now, let X be the number of couples that birth same day
P(X ≥ 1) =
1 − P(X = 0) =
P(X ≥ 1) = 1
Answer:
a) 0.0392
b) 0.4688
c) At least $39,070 to be among the 5% most expensive.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?
This is the pvalue of Z when X = 20000. So
has a pvalue of 0.0392.
So this probability is 0.0392.
b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?
This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.
X = 30000
has a pvalue of 0.5080.
X = 20000
has a pvalue of 0.0392.
So this probability is 0.5080 - 0.0392 = 0.4688
c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?
This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.
The wedding would have to cost at least $39,070 to be among the 5% most expensive.