How many ways can 6 people sit on a bench if 3 of them have to sit side by side

Mathematics

1 answer:

pickupchik [31]3 years ago

4 0

Answer:

144 ways

Step-by-step explanation:

Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.

THey can be arranged in 4! ways, which is:

4! = 4 * 3 * 2 * 1 = 24 ways

Now, the 3 persons themselves can be arranged in 3! ways, which is:

3! = 3 * 2 * 1 = 6 ways

Total ways = 4! * 3! = 24 * 6 = 144 ways

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In a newspaper, it was reported that yearly robberies in Springfield were up 25% to 265 in 2013 from 2012. How many robberies we

NeX [460]

Answer: There were 212 robberies in 2012.

Step-by-step explanation:

Since we have given that

Number of robberies in Springfield in 2013 = 265

Rate of growth in 2013 = 25%

We need to find the number of robberies there were in 2012.

Let the number of robberies in 2012 be x

so, According to question,

$\frac{100+25}{100}\times x=265\\\\\frac{125}{100}\times x=265\\\\1.25\times x=265\\\\x=\frac{265}{1.25}\\\\x=212$

Hence, there were 212 robberies in 2012.

3 0

3 years ago

A scientists has a container of %2 acid solution and a container of 5% acid solution. How many fluid ounces of each concentratio

sergij07 [2.7K]

Answer: 15 oz of 2% solution and 10 oz of 5% solution

<u>Step-by-step explanation:</u>

Set up a table with the given information. <em>Multiply across and add down</em>. The bottom row (Total) will provide the equation. Then, solve the equation for the variable (2% solution) and substitute that value into the quantity for the 5% solution to find that value.

$\begin {array}{l|c|c||l}&Quantity&Percent&Qty\times Percent\\ Solution\ A&x&2\%=0.02&\qquad 0.02(x)=0.02x\\Solution\ B&25-x&5\%=0.05&0.05(25-x)=1.25-0.05x\\Total&25&3.2\%=0.032&0.02x+1.25-0.05x\\\end{array} \\\\\\.\qquad 25(0.32) = 1.25-0.03x\\.\qquad \qquad -0.8 = 1.25 - 0.03x\\.\qquad \quad \ -0.45 = -.03x\\.\qquad \qquad \ 15 = x\\\\Solution\ A: x = 15\\Solution\ B: 25 - x = 25 - (15) = 10$