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dalvyx [7]
3 years ago
13

Alfonse and Melinda are taking a drive in a certain country. They know that a speed of 100 kilometers per hour is approximately

equal to 62 miles per hour. They are now driving on a road that has a speed limit of 105 kilometers per hour. How many miles per hour is the speed​ limit?
Mathematics
1 answer:
Alborosie3 years ago
5 0

Answer:

65.1 miles per hour

Step-by-step explanation:

According to the question 100 Km/hour = 63 miles/hour

It means in one hour 100 Km is traveled which is also equal to 62 miles.

hence 100 Km = 62 miles

dividing both sides by 100 we have

100/100 Km = 62/100 miles

Hence we can say that

1 Km = 0.62 miles

_________________________________________________

Multiplying both side by 105  we have

1 Km * 105 = 0.62 miles * 105

105 Km = 65.1 miles

Thus, 105 Km/hour is same as 65.1 miles per hour.

As 105 kilometres per hour is the speed limit in terms of yards/hour

speed limit will be  65.1 miles per hour.

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erastova [34]

Answer:

The probability is \frac{56!}{64!}

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, 64 \choose 8 .

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function  f : A \rightarrow A , with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}

7 0
2 years ago
<img src="https://tex.z-dn.net/?f=7%20%7Bx%7D%5E%7B3%7D%20%20%2B%204x%20-%205%20%2B%208%20%7Bx%7D%5E%7B5%7D%20" id="TexFormula1"
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Answer:

D

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of a term within the polynomial.

Given

7x³ + 4x - 5 + 8x^{5}

The term with the largest exponent is 8x^{5} with exponent 5

Thus the polynomial is of degree 5 → D

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2 years ago
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