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2 years ago

Alicia has 6 paintings she wants to hang side by side on her wall.

Mathematics

1 answer:

gayaneshka [121]2 years ago

3 0

Answer:

A) 720 ways

B) 15 ways

C) 6 ways

Step-by-step explanation:

A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:

6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

Alicia can arrange her paintings in 720 ways.

B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:

$P(n, r) = \frac{n!}{r!(n-r)!}$

$= \frac{6!}{4!(6-4)!} = 15$

Therefore, Alicia can choose any 4 of her paintings in 15 ways.

C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways

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9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

ozzi

Answer:

You'd be $2 * 10^{-6}$ times tall

Step-by-step explanation:

Given

Represent the previous and new diameter by D1 and D2;

$D_1 = 2 * 10^{-8}m$

$D_2 = 1\ cm$

To determine how tall you'd be, we need to divide D2 by D1;

$Ratio = \frac{D_2}{D_1}$

Substitute values for D2 and D1

$Ratio = \frac{2 * 10^{-8}m}{1\ cm}$

Convert cm to m

$Ratio = \frac{2 * 10^{-8}m}{1 * 0.01\ m}$

$Ratio = \frac{2 * 10^{-8}m}{0.01\ m}$

Convert denominator to exponents

$Ratio = \frac{2 * 10^{-8}m}{10^{-2}\ m}$

$Ratio = \frac{2 * 10^{-8}}{10^{-2}}$

Apply Law of indices

$Ratio = 2 * 10^{-8} * 10^2$

$Ratio = 2 * 10^{-8+2}$

$Ratio = 2 * 10^{-6}$

Hence;

You'd be $2 * 10^{-6}$ times tall

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2 years ago

Kenny types 280 words. How long did he type for? A.4 B. 5 C.6 D. 7

zlopas [31]

Are you sure you didn’t miss anything while writing the question?

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2 years ago

Read 2 more answers

An ant begins at the top of the pictured octahedron. If the ant takes two "steps", what is the probability it ends up at the bot

Aleksandr-060686 [28]

Answer:

$P_{bottom}=\frac{1}{4}=0.25$

Step-by-step explanation:

Starting from the top, the ant can only take four different directions, all of them going down, every direction has a probability of 1/4. For the second step, regardless of what direction the ant walked, it has 4 directions: going back (or up), to the sides (left or right) and down. If the probability of the first step is 1/4 for each direction and once the ant has moved one step, there are 4 directions with the same probability (1/4 again), the probability of taking a specific path is the multiplication of the probability of these two steps:

$P_{2steps}=\frac{1}{4}*\frac{1}{4}=\frac{1}{16}$

There are only 4 roads that can take the ant to the bottom in 2 steps, each road with a probability of 1/16, adding the probability of these 4 roads:

$P_{bottom}=\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}$

The probability of the ant ending up at the bottom is $\frac{1}{4}$ or 0.25.

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2 years ago

Peyton plans to deposit her next paycheck into her savings account.she makes $12.50 per hour and her next paycheck will be h hou

Snowcat [4.5K]

Answer: Current savings account balance

Step-by-step explanation:

since the equation is y = mx + b

mx would be the starting point so she earns 12.50 per hour so it's the current amount she has is 12.50.

Sorry if it dosen't make sense.

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2 years ago

Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year,

IrinaVladis [17]

Use compound interest formula F=P(1+i)^n twice, one for each deposit and sum the two results.

For the P=$40,000 deposit,
i=10%/2=5% (semi-annual)
number of periods (6 months), n = 6*2 = 12
Future value (at end of year 6),
F = P(1+i)^n = 40,000(1+0.05)^12 = $71834.253

For the P=20000, deposited at the START of the fourth year, which is the same as the end of the third year.
i=5% (semi-annual
n=2*(6-3), n = 6
Future value (at end of year 6)
F=P(1+i)^n = 20000(1+0.05)^6 = 26801.913

Total amount after 6 years
= 71834.253 + 26801.913
=98636.17 (to the nearest cent.)

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2 years ago