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3 years ago

light travels 1.18 x 10^10 inches in 1 second. About how far will light travel in 1 minute? Use scientific notation.

Mathematics

1 answer:

drek231 [11]3 years ago

7 0

Answer: $4.248*10^{13}\ seconds$

Step-by-step explanation:

We must remember that, by definition, Scientific notation has the following form:

$a*10^b$

Where $1\leq |a|$ and "b" is an integer.

Let be "x" the distance light will travel in 1 minute.

According to the information provided in the exercise, the light travels $1.18 * 10^{10}\ inches$ per second.

We know that:

$1\ minute=3,600\ seconds$

To write this in Scientific notation, move the decimal point three places to the left:

$3.6*10^3\ seconds$

Then, we can set up the following proportion:

$\frac{1.18 * 10^{10}}{1}=\frac{x}{3.6*10^3}$

Solve for "x" (We must remember the Product of powers property: $a^m*a^n=a^{mn}$ ):

$(3.6*10^3)(\frac{1.18 * 10^{10}}{1})=x\\\\x=4.248*10^{13}\ seconds$

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There are n questions on a multiple choice exam, and for each question, there are four choices. To pass the exam, one must corre

irinina [24]

Answer:

a) 0.352% probability of the student passing

b) 5

c) 1.875

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student answers it correctly, or he answers it wrong. The probability of correctly answering a question is independent from the probability of correctly answering other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

For each question, there are four choices.

One choice is correct, so $p = \frac{1}{4} = 0.25$

a. Find the probability of the student passing for n = 10.

0.7*10 = 7

This is $P(X \geq 7)$ when $n = 10$

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031$

$P(X = 8) = C_{10,8}.(0.25)^{8}.(0.75)^{2} = 0.0004$

$P(X = 9) = C_{10,9}.(0.25)^{9}.(0.75)^{1} = 0.00002$

$P(X = 10) = C_{10,10}.(0.25)^{10}.(0.75)^{0} \cong 0$

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0031 + 0.0004 + 0.00002 = 0.00352$

0.352% probability of the student passing

b. Find the expected number of questions answered correctly for n = 20.

Here we have n = 20. So

$E(X) = np = 20*0.25 = 5$

c. Find the variance for the number of questions answered correctly for n = 10.

Here we have n = 10.

$V(X) = np(1-p) = 10*0.25*0.75 = 1.875$

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4 years ago

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AnnyKZ [126]

Answer:

$r \cdot 4 = z$

Step-by-step explanation:

An expression means that we don't know enough to create an equation. So, this means we will mostly be using variables.

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$r \cdot 4 = z$

r = how much he runs per day

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This is your expression!

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3 years ago

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Ira Lisetskai [31]

Area of semicircle is given by:
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Murljashka [212]

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Step-by-step explanation:

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light travels 1.18 x 10^10 inches in 1 second. About how far will light travel in 1 minute? Use scientific notation.​

light travels 1.18 x 10^10 inches in 1 second. About how far will light travel in 1 minute? Use scientific notation.