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3 years ago

15

Adam rolls a number cube with faces numbered 1 to 6. what is the probability, to the nearest hundredth, that he rolls a 4?

1 answer:

AURORKA [14]3 years ago

4 0

To solve this problem, let us first define probability. We know in statistics class that probability is simply the ratio of a selected event to occur over the total number of events. That is:

probability = number of selected event to occur / total number of events

In this scenario, our only selected event to occur is to have a dice roll of 4. That is 1 event only. Now since there are 6 number in the dice, therefore the total number of events is 6. Therefore:

probability = 1 / 6

probability = 0.1666667

Rounding off to the nearest hundredth:

<span>probability = 0.17</span>

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If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

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Martin burns 360 calories running for 30 minutes. Paul burns 165 calories for every 15 minute he runs. If Kara runs for 20 minut

Yanka [14]

Answer: She would have to burn between 220 and 240 calories per minute to have a calorie burn rate between those of Martin and Paul.

Step-by-step explanation:

Martin:

360 calories / 30 min = 12 calories/min

Paul:

165 calories / 15 min = 11 calories/min

Kara:

Needs to burn between 11 and 12 calories/min, so we'll calculate the range:

11 calories/min x 20 min = 220 calories (minimum # calories she can burn)

12 calories/min x 20 min = 240 calories (maximum # calories she can burn)

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