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3 years ago

Amaryn bought 8 notebooks. each notebook is 12.78 Amaryn paid 5.99 for shipping

Mathematics

1 answer:

Anit [1.1K]3 years ago

7 0

Answer:

108.23

Step-by-step explanation:

8*12.78=102.24+5.99= 108.23

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What is the sum of the measures of the interior angles of this heptagon? A 7-sided figure. 720 degrees 900 degrees 1,080 degrees

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900°

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Running Russell runs 9/10 mile in 5 minutes. How many miles does he run in one minute?

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Answer:

<u>Russell runs 9/50 of a mile or 0.18 miles in one minute.</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Distance run by Russell = 9/10 of a mile

Time Russell runs 9/10 of a mile = 5 minutes

2. How many miles does he run in one minute?

Speed of Russell = Distance run by Russell / Time Russell runs

Speed of Russell = (9/10) / 5

Speed of Russell = 9/10 * 1/5 = 9/50

Russell runs 9/50 of a mile in one minute. If we want to express the answer in decimals, we have : 9/50 = 0.18

<u>Russell runs 9/50 of a mile or 0.18 miles in one minute</u>

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3 years ago

Using a 52 card deck, how many 5 card hands have either 5 hearts or 4 hearts and 1 club

777dan777 [17]

Answer:

10,582

Step-by-step explanation:

We can choose 5 cards from 52 card deck in

$n = \binom{52}{5} = \frac{52!}{5!(52-5)!} = \frac{52!}{5!47!} = \frac{\cancel{47!} \cdot 48 \cdot 49 \cdot 50 \cdot 51 }{5! \cancel{47!}} = \frac{ 48 \cdot 49 \cdot 50 \cdot 51 }{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} = 2 \; 598 \; 960$

ways.

Now, let's calculate the number of ways we can choose 5 hearts. We know that in a 52 card deck, we have 13 hearts. Therefore, the number of ways to choose 5 hearts is

$n_1 = \binom{13}{5} = \frac{13!}{5!(13-5)!} = \frac{13!}{5!8!} = \frac{8! \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{5!8!} = \frac{9 \cdot 10 \cdot 11 \cdot 12 \cdot 13}{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} = 1287$

Similarly, number of ways to choose 4 hearts equals $\binom{13}{4}$ and number of ways to choose 1 club equals $\binom{13}{1}$ , since there are also 13 clubs in the deck.

Therefore, the number of ways of choosing 4 hearts and 1 club equals

$n_2 = \binom{13}{4} \cdot \binom{13}{1} = 9295$

The probability of this event is calculated as

$P(A) = \frac{\text{total number of ways to choose 5 hearts or 4 hearts and a club}}{\text{total number of ways to choose 5 cards from a deck of 52 cards}}$

Therefore

$P(A) = \frac{n_1+n_2}{n} = \frac{1287+9295}{2598960} =0.0040716 \approx 0.0041$

5 0

3 years ago