What is log Subscript 15 Baseline 2 cubed rewritten using the power property?

A quarter is approximately 0.07 inches thick. A dollar bill is approximately 4.3 × 10-3 inches thick.

lawyer [12517]

m = 6.57 and n = -2

Detailed explanation:

To solve this question, convert the thickness of a dollar bill into standard notation and compare the two thicknesses.

0.07 compared to 0.0043 results in 0.0657

0.0657 = 6.57 x 10^-2

Thus, a quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2

8 0

2 months ago

The tiles that Bruce used were each of a square foot in the area. The table shows the area covered by Felicia’s tiles in terms o

zzz [12365]

Response:

Step-by-step explanation:

We need to form an equation that illustrates the area that Felicia has covered, denoted as y, in relation to the number of tiles she utilized, represented by x.

Let x= Number of tiles

y=Area occupied by Felicia's tiles

$x_1=9, x_2=18, x_3=27$

$y_1=1, y_2=2,y_3=3$

$\frac{x_1}{y_1}=\frac{9}{1}=9$

$\frac{x_2}{y_2}=\frac{18}{2}=9$

$\frac{x_3}{y_3}=\frac{27}{3}=9$

The relationship between x and y is constant. Hence, it follows a direct proportion.

The equation for direct proportion is shown as

$\frac{x}{y}=k$

Where

k=The value of the ratio of x and y

x and y are variable factors

Here, we have k=9

Substituting the known values into the equation

leads us to

$\frac{x}{y}=9$

$x=9y$

$y=\frac{1}{9}x$

This represents the necessary equation depicting the area Felicia covered, y, in terms of the number of tiles utilized, x.

6 0

2 months ago

One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilit

tester [12383]

Answer:

a) Robot Reliability = 0.7876

b1) Component 1: 0.8034

Component 2: 0.8270

Component 3: 0.8349

Component 4: 0.8664

b2) To maximize overall reliability, Component 4 should be backed up.

c) To achieve the highest reliability of 0.8681, backup for Component 4 with a reliability of 0.92 should be implemented.

Step-by-step explanation:

Component Reliabilities:

Component 1 (R1): 0.98

Component 2 (R2): 0.95

Component 3 (R3): 0.94

Component 4 (R4): 0.90

a) The reliability of the robot can be determined by calculating the reliabilities of the individual components that constitute the robot.

Robot Reliability = R1 x R2 x R3 x R4

= 0.98 x 0.95 x 0.94 x 0.90

Robot Reliability = 0.787626 ≅ 0.7876

b1) As only a single backup can be used at once, and its reliability matches that of the original, we evaluate each component's backup sequentially:

Robot Reliability with Component 1 backup is calculated by first assessing the failure probability of the component plus its backup:

Failure probability = 1 - R1

= 1 - 0.98

= 0.02

Combined failure probability for Component 1 and backup = 0.02 x 0.02 = 0.0004

Thus, reliability of combined Component 1 and backup (R1B) = 1 - 0.0004 = 0.9996

Robot Reliability = R1B x R2 x R3 x R4

= 0.9996 x 0.95 x 0.94 x 0.90

Robot Reliability = 0.8034

To determine reliability of Component 2:

Failure probability for Component 2 = 1 - 0.95 = 0.05

Combined failure probability of Component 2 and backup = 0.05 x 0.05 = 0.0025

Reliability of Component 2 with backup (R2B) = 1 - 0.0025 = 0.9975

Robot Reliability = R1 x R2B x R3 x R4

= 0.98 x 0.9975 x 0.94 x 0.90

Robot Reliability = 0.8270

Robot Reliability with backup of Component 3 calculates as follows:

Failure probability for Component 3 = 1 - 0.94 = 0.06

Combined failure probability of Component 3 and backup = 0.06 x 0.06 = 0.0036

Reliability for Component 3 with backup (R3B) = 1 - 0.0036 = 0.9964

Robot Reliability = R1 x R2 x R3B x R4

= 0.98 x 0.95 x 0.9964 x 0.90

Robot Reliability = 0.8349

Robot Reliability with Component 4 backup calculates as:

Failure probability for Component 4 = 1 - 0.90 = 0.10

Combined failure probability of Component 4 and backup = 0.10 x 0.10 = 0.01

Reliability for Component 4 and backup (R4B) = 1 - 0.01 = 0.99

Robot Reliability = R1 x R2 x R3 x R4B

= 0.98 x 0.95 x 0.94 x 0.99

Robot Reliability = 0.8664

b2) The best reliability is achieved with the backup of Component 4, yielding a value of 0.8664. Thus, Component 4 is the best candidate for backup to optimize reliability.

c) A reliability of 0.92 indicates a failure probability of = 1 - 0.92 = 0.08

We can compute the probability of failure for each component along with its backup:

Component 1 = 0.02 x 0.08 = 0.0016

Component 2 = 0.05 x 0.08 = 0.0040

Component 3 = 0.06 x 0.08 = 0.0048

Component 4 = 0.10 x 0.08 = 0.0080

Thus, the reliabilities for each component and its backup become:

Component 1 (R1BB) = 1 - 0.0016 = 0.9984

Component 2 (R2BB) = 1 - 0.0040 = 0.9960

Component 3 (R3BB) = 1 - 0.0048 = 0.9952

Component 4 (R4BB) = 1 - 0.0080 = 0.9920

Reliability of robot including backups for each of the components can be calculated as:

Reliability with Backup for Component 1 = R1BB x R2 x R3 x R4

= 0.9984 x 0.95 x 0.94 x 0.90

Reliability with Backup for Component 1 = 0.8024

Reliability with Backup for Component 2 = R1 x R2BB x R3 x R4

= 0.98 x 0.9960 x 0.94 x 0.90

Reliability with Backup for Component 2 = 0.8258

Reliability with Backup for Component 3 = R1 x R2 x R3BB x R4

= 0.98 x 0.95 x 0.9952 x 0.90

Reliability with Backup for Component 3 = 0.8339

Reliability with Backup for Component 4 = R1 x R2 x R3 x R4BB

= 0.98 x 0.95 x 0.94 x 0.9920

Reliability with Backup for Component 4 = 0.8681

To maximize overall reliability, Component 4 should be backed up at a reliability of 0.92, achieving an overall reliability of 0.8681.

4 0

3 months ago