Sarah used her calculator to work out the value of a number y .

Mathematics

1 answer:

mars1129 [50]3 years ago

5 0

Answer:

$7.75 \: \leqslant y \: < \: 7.85$

Step-by-step explanation:

The calculator approximated the value of y at 7.8.

We need to complete the error interval for y.

In other words, we calculate the upper and lower bound for y.

The level level of accuracy is to the nearest tenth.

To find the lower bound, we subtract half the degree of accuracy to get:

$y \geqslant 7.8 - 0.05 \\ y \geqslant 7.75$

To find the upper bound, add half the level of accuracy to get:

$y \: < \: 7.8 + 0.05 \\ y \: < \: 7.85$

Therefore the error interval is

$7.75 \: \leqslant y \: < \: 7.85$

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Simplify the following expression:

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$\frac{4}{ \frac{1}{4} - \frac{5}{2} }$

To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator. To make them compatible, we can convert $\frac{5}{2}$ into $\frac{10}{4}$ :

$\frac{4}{ \frac{1}{4} - \frac{5}{2}( \frac{2}{2}) } = \frac{4}{ \frac{1}{4} - \frac{10}{4} }$

Next, we can simplify:

$\frac{4}{ \frac{1}{4} - \frac{10}{4} } = \frac{4}{ -\frac{9}{4}}$

Finally, to cancel the denominator within the denominator, we can multiply the whole expression by $\frac{4}{4}$ , or 1:

$\frac{4}{ -\frac{9}{4}}* \frac{4}{4} = -\frac{16}{9}$

The expression simplifies to $-\frac{16}{9}$ , or $-1 \frac{7}{9}$ as a mixed number.