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3 years ago

5

Tom and 29 friends (30 total) are to sit in three rows of 10 at a movie theatre. They madea rule that Within each row, they must

sit in order of tallest to shortest with the tallestperson on the left. Given that there are no two people with the same height and there areno restrictions on where a person must sit, how many different seating arrangements arepossible

1 answer:

Phoenix [80]3 years ago

6 0

Answer:

The answer is "6000".

Step-by-step explanation:

It seems to be a total of 30 buddies there. Every column has 10 seats so that the 10 pals are now in a row. Of all the other 20 buddies, 10 are on the following row. And we have ten friends remaining and that they are sitting in the next row.

Therefore the possibility of sitting is:

$30 \times 20 \times 10 = 6000$

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4 years ago

Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)

BARSIC [14]

Answer:

14.20669 years

Roughly 14 years and 2.5 months.

Step-by-step explanation:

Assuming this is compound interest.

The formula is $A=P(1+\frac{r}{n})^{nt}$

$A=$ Final Amount

$P=$ Principal Amount

$r=$ Interest Rate

$n=$ # of times interest is compounded per year

$t=$ Time in years

We are looking for the times in years to double the money so

$2500*2=5000$

$A=5000$

$P=2500$

$r=0.05$

$n=1$

$t=?$

Lets solve for $t$ .

Step 1.

Plug in our numbers into the compound interest formula.

$5000=2500(1+\frac{0.05}{1}) ^{1*t}$

Step 2.

Simplify the equation.

Evaluate $1+\frac{0.05}{1}=1.05$

Evaluate $1*t=t$

$5000=2500(1.05) ^{t}$

Step 3.

Divide both sides of the equation by $2500$

$\frac{5000}{2500}=1.05 ^{t}$

Evaluate $\frac{5000}{2500}=2$

$2=1.05 ^{t}$

Step 4.

Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.

$ln(2)=t*ln(1.05)$

Step 5.

Divide both sides of the equation by $ln(1.05)$

$\frac{ln(2)}{ln(1.05)}=t$

Step 6.

Evaluate

$t=14.20669$

Roughly 14 years and 2.5 months.

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