Anthony practices swimming by completing 10 laps every ay every time he practices he improves his time by 3 seconds if it took A
2 answers:
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Answer:
a) 9.52% probability that, in a year, there will be 4 hurricanes.
b) 4.284 years are expected to have 4 hurricanes.
c) The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
6.9 per year.
This means that
a. Find the probability that, in a year, there will be 4 hurricanes.
This is P(X = 4).
So
9.52% probability that, in a year, there will be 4 hurricanes.
b. In a 45-year period, how many years are expected to have 4 hurricanes?
For each year, the probability is 0.0952.
Multiplying by 45
45*0.0952 = 4.284.
4.284 years are expected to have 4 hurricanes.
c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here?
The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
Answer:
1. triangle TCA ~ triangle GOD
4. If TC/GD=3/2, then m<T/m<G=3/2.
Step-by-step explanation:
<u><em>The statements of the question are</em></u>
1. triangle TCA ~ triangle GOD
2. AT: OG= AC:OD
3. If TC/GD=3/2, then AC/OD=3/2.
4. If TC/GD=3/2, then m<T/m<G=3/2.
5. If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3.
6. If AC is twice as long as AT, then OD is twice as long as OG
<u><em>Verify each statement</em></u>
1) triangle TCA ~ triangle GOD
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
triangle CAT ~ triangle DOG -----> is given
so
Reorder
Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement
triangle TCA ~ triangle GDO
therefore
The statement is not correct
2). AT: OG= AC:OD
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
triangle CAT ~ triangle DOG -----> is given
so
Applying proportion
The statement is true
3). If TC/GD=3/2, then AC/OD=3/2.
we have that
---> see part 2)
so
therefore
The statement is true
4). If TC/GD=3/2, then m<T/m<G=3/2
Remember that
In two similar triangles, corresponding angles are congruent
so
therefore
The statement is false
5). If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3
we know that
If the scale factor of triangle CAT to triangle DOG is a/b. then the scale factor of triangle DOG to triangle CAT is b/a
The scale factor will be the reciprocal
therefore
The statement is true
6). If AC is twice as long as AT, then OD is twice as long as OG
we know that
Reorder
If AC is twice as long as AT ----> AC=2AT
If OD is twice as long as OG ----> OD=2OG
substitute
simplify
----> is true
therefore
The statement is true
Answer:
Step-by-step explanation:
<u>Speed</u>
The speed is the ratio between the distance x traveled by an object and the time t taken.
The car travels x=43 Km in t=56 minutes. We are required to express the speed in Km/h. The time needs to be expressed in hours:
Now apply the formula: