Jaimie is looking for a golf ball that he hit into the air towards a fence surrounding the golf course. The fence has a height o

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:

The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.

The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.

Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.

b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.

The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.

Answer:

Step-by-step explanation:

Given:

• Fuel volume = 5/6
• Each trip uses fuel = 1/12
• Number of trips to work = x

Since 1/12 of the tank is used for each trip and the starting volume is 5/6, the equation can be represented as:

By solving the equation, we find:

• x = ÷
• x = × 12
• x = 10

This means Felitz can make 10 trips to/from work with a tank filled to 5/6.

Answer:

The scale factor equates to 3.

Detailed explanation:

Please refer to the provided image for clarity regarding this issue.

We know that

If two shapes are similar, then the ratio of their areas corresponds to the square of the scale factor.

Let

z -----> scale factor

x -----> area of polygon Q

y ----> area of polygon P

Thus, we have

so, we proceed with

Determining the area of polygon Q

The polygon Q can be divided into five distinct squares.

Refer to the additional figure N 2.

The area of polygon Q, which represents the total area of the five squares, is

Calculating the scale factor

Thus, we derive

By substituting the values, we find

Taking the square root of both sides results in

Thus,

The scale factor resolves to 3.

Response:

The area of the shaded part is 42.50 cm².

Detailed explanation:

Examine the diagram provided.

The circle has a radius of r = 5 cm.

Dimensions of the rectangle are:

l = 11 cm

b = 11 cm.

Calculate the area of the shaded portion as follows:

Area of the shaded region = Area of rectangle - Area of circle

Consequently, the shaded area totals 42.50 cm².