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2 years ago

10

The area of an oil spill is doubling in size every day. At the start of the day on May 1, the oil spill covers 20 square meters.

During which day will the area exceed 500 square meters?

1 answer:

ozzi2 years ago

5 0

Answer:

May 6

Step-by-step explanation:

20 x 2 = 40 40 x 2 = 80 80 x 2 = 160 x 2 = 320 320 x 2 = 640 after 5 days on may 6 it will surpass 500 meters.

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A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24(Three-hal

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Answer:

$f(x)=16\, (\frac{3}{2} )^{x-1}$

Step-by-step explanation:

Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ( $a$ ) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:

$f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4$

Since we are given the information that $f(5)=81$ we can use this to find the value of the first term:

$f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16$

Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:

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100 random samples were taken from a large population. A particular numerical characteristic of sampled items was measured. The

Marta_Voda [28]

Answer:

The median is $Median = 0.903$

Step-by-step explanation:

From the question we are told that

The sample size is n = 100

The $1^{st} \to 45^{th}$ measurements is $= 0.859 \to 0.900$

Generally since that after 0.900 we have 0.901 , then the

$46^{th} \ measurement \ is \ 0.901$

in the same manner the $47^{th} \ measurement \ is \ 0.902$ ,

Given that 0.902 was observed three times it means that

$47^{th},48^{th},49^{th} \ measurement \ is \ 0.902$ ,

Given that 0.903 was observed two times it means that

$50^{th},51^{th} \ measurement \ is \ 0.903$ ,

Given that 0.903 was observed four times it means that

$52^{nd},53^{rd},54^{th},55^{th} \ measurement \ is \ 0.904$ ,

Given that the highest measurement is 0.958 then then the $56^{th} \to 100^{th} \ measurement \ is \ between \ 0.905 \to 0.958$

Generally the median is is mathematically represented as

$Median = \frac{ [\frac{n^{th}}{2}] + [(\frac{n}{2})^{th} + 1 ]}{2}$

=> $Median = \frac{ [\frac{100^{th}}{2}] + [(\frac{100}{2})^{th} + 1 ]}{2}$

=> $Median = \frac{ [50^{th}] + [51^{th} ]}{2}$

=> $Median = \frac{ 0.903 + 0.903}{2}$

=> $Median = 0.903$

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2 years ago