Brian compared the absolute values of the numbers−12,34,and−14.Arrange the numbers from least to greatest.

Fale runs each lap in 6 minutes. He will run at most 30 minutes today. What are the possible numbers of laps he will run today?

fgiga [73]

The answer is 5. 30 divide 6=n. In the question it said Fale will run 30 minutes today, and if he can run a lap in 6 minute, you will have to divide to get the answer, which is n or 5.

7 0

3 years ago

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A whole number has the first four odd prime numbers as its factors. What is the smallest value this whole number could be?

liberstina [14]

Answer:

d. 210

Step-by-step explanation:

First four distinct prime numbers = 2,3,5,7

2×3×5×7 = 210

HOPE IT HELPS!!

5 0

3 years ago

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In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year. Let X be the number of quakes in a given

hichkok12 [17]

Answer:

a) Earthquakes are random and independent events.

b) There is an 85.71% probability of fewer than three quakes.

c) There is a 0.51% probability of more than five quakes.

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.

In this problem, we have that:

In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year, so $\mu = 1.3$

(a) Justify the use of the Poisson model.

Earthquakes are random and independent events.

You can't predict when a earthquake is going to happen, or how many are going to have in a year. It is an estimative.

(b) What is the probability of fewer than three quakes?

This is $P(X < 3)$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = \frac{e^{-1.3}*1.3^{0}}{(0)!} = 0.2725$

$P(X = 1) = \frac{e^{-1.3}*1.3^{1}}{(1)!} = 0.3543$

$P(X = 2) = \frac{e^{-1.3}*1.3^{2}}{(2)!} = 0.2303$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2725 + 0.3543 + 0.2303 = 0.8571$

There is an 85.71% probability of fewer than three quakes.

(c) What is the probability of more than five quakes?

This is $P(X > 5)$

We know that either there are 5 or less earthquakes, or there are more than 5 earthquakes. The sum of the probabilities of these events is decimal 1.

So

$P(X \leq 5) + P(X > 5) = 1$

$P(X > 5) = 1 - P(X \leq 5)$

In which

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

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

$P(X = 0) = \frac{e^{-1.3}*1.3^{0}}{(0)!} = 0.2725$

$P(X = 1) = \frac{e^{-1.3}*1.3^{1}}{(1)!} = 0.3543$

$P(X = 2) = \frac{e^{-1.3}*1.3^{2}}{(2)!} = 0.2303$

$P(X = 3) = \frac{e^{-1.3}*1.3^{3}}{(3)!} = 0.0980$

$P(X = 4) = \frac{e^{-1.3}*1.3^{4}}{(4)!} = 0.0324$

$P(X = 5) = \frac{e^{-1.3}*1.3^{5}}{(5)!} = 0.0084$

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.2725 + 0.3543 + 0.2303 + 0.0980 + 0.0324 + 0.0084 = 0.9949$

Finally

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9949 = 0.0051$

There is a 0.51% probability of more than five quakes.

5 0

3 years ago

18. One scoop of rice weighs about 3' milligrams.

Vladimir79 [104]

Answer:

Step-by-step explanation:

b. 1 grain in one scoop. if one scoop is 3 milligrams and 1 grain is 3 milligrams, then there is 1 grain in one scoop.

4 0

3 years ago

The total distance a ball rolls varies directly with the time in seconds. The ball rolls a total distance of 112 centimeters in

Komok [63]

Answer:

25 s

Step-by-step explanation:

25 times 28 is 700

8 0

3 years ago