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3 years ago

Find the range of the given data set. 5/8, 3/4, 1 1/8, 1 1/4 A)5/8 B)3/4 C)1 1/8

Mathematics

1 answer:

rodikova [14]3 years ago

6 0

Answer:

A)5/8

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

Given data set:

5/8, 3/4, 1 1/8, 1 1/4

Rewriting the data set in the same denominator to compare:

5/8, 6/8, 9/8, 10/8

As we see the smallest value is 5/8 and the highest value is 10/8, so the difference:

10/8 - 5/8 = 5/8

So, the range of the given data set is 5/8

Correct choice is: A)5/8

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Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

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So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

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The formula for rectangle is given as:

$\text { area of rectangle }=length \times width$

As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

On solving quadratic equation by using quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

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