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Vikki [24]
3 years ago
12

An athlete runs around a circular track. The track has a diameter of 200 feet. How many laps does she need to take to run a mile

?
Mathematics
1 answer:
Shtirlitz [24]3 years ago
3 0
First you have to figure out the length of the track:

2 * \pi * r

r is the half of the diameter:
200ft : 2 = 100ft

2* \pi *100ft = 200\pi≈ 628,31

The athlete has to run ca. 5280ft for one mile:

5280 : 628,31≈8,4

The athlete has to run 8,4 laps
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3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters
Veseljchak [2.6K]

Answer:

Since the order of choice matters, we will permute the values.                       a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___  ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_<u>4</u>_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with  3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_<u>4</u>_ <u>_3_</u> ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_<u>4</u>_ _<u>3</u>_ _<u>2</u>_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

8 0
2 years ago
156 divided by 12 equals?
Sergeu [11.5K]
156/12 = 12 * 13/12 = 13 :D
3 0
3 years ago
Read 2 more answers
g A fair coin is tossed 20 times. The number of heads observed is the count X of successes. Give the distribution of X . Choose
Nuetrik [128]

Answer:

We assume that we have a fair coin that is p(Head)=p(Tails)=0.5

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

X \sim Binom(n=20, p=0.5)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

Solution to the problem

We assume that we have a fair coin that is p(Head)=p(Tails)=0.5

For this case we define the random variable X as "number of heads observed in 20 times". The distribution for X is given by:

X \sim Binom(n=20, p=0.5)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

3 0
2 years ago
11) In a triangle, the ratio of the measures of three angles is 2:5:8. Find the measures of
natta225 [31]

Answer:

Sum of interior angles of a triangle always = 180 degrees

add the individual ratios to get a sum composite ratio:

2+5+8 = 15

180 / 15 = 12

Multiply individual ratios:

{2:5:8} * 12 = 24:60:96

Check:

24 + 60 + 96 = 180

Step-by-step explanation:

I hope it's help

7 0
2 years ago
Use your calculator to select the best answer below:
bixtya [17]

Answer:

-2\sqrt{a}

Step-by-step explanation:

\lim_{x \to a} \frac{a-x}{\sqrt{x} -\sqrt{a} } \\ =-\lim_{x \to a} \frac{x-a}{\sqrt{x} -\sqrt{a} }  \\=-\lim_{x \to a} \frac{(\sqrt{x} -\sqrt{a})(\sqrt{x} +\sqrt{a})}{\sqrt{x} -\sqrt{a} }  \\=- \lim_{x \to a} \sqrt{x} +\sqrt{a}\\=-2\sqrt{a}

6 0
2 years ago
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