The perimeter = 4 * length of a semicircle of radius 5 == 4* pi * 5 = 20 pi cm

The area of one of the clear parts = 1/2 area of square - area semicircle

= 1/2 * 10^2 - 1/2 pi *5^2 = 50 - 12.5pi

So area of shaded parts = area of square - 4 (50 - 12.5pi)
= 100 - 200 + 100pi = (100pi - 100) cm^2

6 0

3 years ago

An item costs x dollars and then a 20% discount is applied

Marat540 [252]

Answer:

If an item is x dollars and 20% discount is applied, the new price will be: 0.8x

Step-by-step explanation:

100 - 20%(20) = 80

80 = 80% or 0.8

So, the remaining of the price of x will be 0.8x.

7 0

2 years ago

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters,

tiny-mole [99]

Answer:

Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.

Step-by-step explanation:

We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.

A random sample of 39 steel bolts is selected.

Let $\bar X$ = sample mean diameter

The z score probability distribution for sample mean is given by;

Z = $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }$ ~ N(0,1)

where, $\mu$ = population mean diameter = 141 millimetres

$\sigma$ = standard deviation = 7 millimetres

n = sample of steel bolts = 39

Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P( $\bar X$ > 141.4 millimetres)

P( $\bar X$ > 141.4) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }$ > $\frac{141.4-141}{\frac{7}{\sqrt{39} } } }$ ) = P(Z > 0.36) = 1 - P(Z $\leq$ 0.36)

= 1 - 0.6406 = 0.3594

The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.

8 0

3 years ago