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2 years ago

What is the 72nd term of -27, -11, 5

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

5 0

Answer:

1109

Step-by-step explanation:

The first term is -27, and the common difference is 16.

The nth term is:

a = a₁ + d (n − 1)

a = -27 + 16 (n − 1)

a = -27 + 16n − 16

a = 16n − 43

The 72nd term is:

a = 16(72) − 43

a = 1109

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Statistics from the Riverside Police Department show that in the last 12 years there were 648 reported crimes in the city. Find

Sav [38]

Answer:

12.76% probability that there is exactly 1 reported crime on any given day.

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Statistics from the Riverside Police Department show that in the last 12 years there were 648 reported crimes in the city.

Each year has 365 days. We want the mean for a day. So

$\mu = \frac{648}{12*365} = 0.1479$

Find the probability that there is exactly 1 reported crime on any given day.

This is P(X = 1).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 1) = \frac{e^{-0.1479}*(0.1479)^{1}}{(1)!} = 0.1276$

12.76% probability that there is exactly 1 reported crime on any given day.

6 0

2 years ago

Christopher’s hourly salary is $15. If Christopher works 7 hours a day, then how much will be earned in a day?

suter [353]

7 times 15 = 105. Hope it helps

5 0

2 years ago

A company paid $48 for 2 cases of printer paper. each case contained 12 packages of paper. next month the company’s office manag

enyata [817]

Cost would be $4,320.

6 0

3 years ago

Pleeeeeeeeeeesease helllllllp meee

andrew-mc [135]

Answer:

This is a vertical angle theorem

Step-by-step explanation:

Vertical angles are a pair of opposite angles formed by intersecting lines. In the figure, ∠1 and ∠3 are vertical angles. ... Vertical angles are always congruent . So, in this figure, ∠1≅∠3 and ∠2≅∠4 .

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2 years ago

Modeling Radioactive Decay In Exercise, complete the table for each radioactive isotope.

Travka [436]

Answer :

The amount after 1000 years will be, 5.19 grams.

The amount after 10000 years will be, 0.105 grams.

Step-by-step explanation :

Half-life = 1599 years

First we have to calculate the rate constant, we use the formula :

$k=\frac{0.693}{t_{1/2}}$

$k=\frac{0.693}{1599\text{ years}}$

$k=4.33\times 10^{-4}\text{ years}^{-1}$

Now we have to calculate the amount after 1000 years.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $4.33\times 10^{-4}\text{ years}^{-1}$

t = time passed by the sample = 1000 years

a = initial amount of the reactant = 8 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

$1000=\frac{2.303}{4.33\times 10^{-4}}\log\frac{8}{a-x}$

$a-x=5.19g$

Thus, the amount after 1000 years will be, 5.19 grams.

Now we have to calculate the amount after 10000 years.

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $4.33\times 10^{-4}\text{ years}^{-1}$

t = time passed by the sample = 10000 years

a = initial amount of the reactant = 8 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

$10000=\frac{2.303}{4.33\times 10^{-4}}\log\frac{8}{a-x}$

$a-x=0.105g$

Thus, the amount after 10000 years will be, 0.105 grams.

4 0

3 years ago