Precision aviation had a profit margin of 6.25%, a total assets turnover of 1.5, and an equity multiplier of 1.8. what was the firm's roe? a. 15.23%b. 16.03%c. 16.88%d. 17.72%e. 18.60%

(a) is more precise

(b) is more accurate

Explanation:

When a given set of values are precise, this implies that all the values are close to each other but may not be accurate. But a set of values are accurate when they are compared and it can be observed that they are close to a given measured value. So we can infer that the values in option (a) are precise, while that in (b) are accurate when compared with the book value given.

+41.50 = 0 10000100 01001100000000000000000  [single precision]

-72.125 = 1 10000000101 0010000010000000000000000000000000000000000000000000 [double precision]

Explanation:

(I) +41.50 using single precision

Follow the following steps:

(a) Single precision has 32 bits in total and is divided into three groups: sign (has 1 bit), an exponent (has 8 bits) and a mantissa (also called fraction, has 23 bits)

(b) Divide the number (41.50) into its whole and decimal parts:

Whole = 41

Decimal = 0.50

(c) Convert the whole part to binary:

2    |    41

2    |    20 r 1

2    |    10 r 0

2    |    5 r 0

2    |    2 r 1

2    |    1 r 0

     |    0 r 1

Reading upwards gives 41 = 101001₂

(d) Convert the decimal part to binary:

0.50 x 2 = 1.0  = 1 [number in front of decimal]

0.0 x 2 = 0.0 = 0  [number in front of decimal]

Reading downwards gives 0.5 = 10₂

(e) Put the two parts together as follows;

    101001.10₂

(f) Convert the result in (e) to its base 2 scientific notation:

Move the decimal to just before the leftmost bit as follows;

1.0100110

In doing so, we have moved over 5 numbers to the left. Therefore, the exponent is 5. Moving to the left gives a positive exponent while moving to the right gives a negative exponent.

Altogether we have;

1.0100110 x 2⁵

(g) Determine the sign bit of the number and display in binary: Since the number +41.50 is positive, the sign bit is 0.

(h) Determine the exponent bits.

Since this is a single precision conversion, the exponent bias is 127.

To get the exponent we add the exponent value from (e) to the exponent bias and get;

5 + 127 = 132

(i) Convert the exponent to binary:

2    |    132

2    |    66 r 0

2    |    33 r 0

2    |    16 r 1

2    |    8 r 0

2    |    4 r 0

2    |    2 r 0

2    |    1 r 0

     |    0 r 1

Reading upwards gives 132 = 10000100₂

(j) Determine the mantissa bits:

The mantissa is the rest of the number after the decimal of the base 2 scientific notation found in (f) above.

0100110 from 1.0100110 x 2⁵                  [Just remove the leftmost 1 and the decimal point]

(k) Combine the three parts: sign bit (1 bit), exponent bits (8 bits) and mantissa bits (23 bits)

sign bit = 0                [1 bit]

exponent bits = 10000100        [8 bits]

mantissa bits = 0100110        [7 out of 23 bits]

Then fill out the remaining part of the mantissa with zeros to make it 23 bits.

mantissa bits = 01001100000000000000000        

Putting all together we have

0 10000100 01001100000000000000000 as +41.50 in  a IEEE 754 single precision format.

(II) -72.125 using double precision

Follow the following steps:

(a) Double precision has 32 bits in total and is divided into three groups: sign (has 1 bit), an exponent (has 11 bits) and a mantissa (also called fraction, has 52 bits)

(b) Divide the number (72.125) into its whole and decimal parts:

Whole = 72

Decimal = 0.125

(c) Convert the whole part to binary:

2    |    72

2    |    36 r 0

2    |    18 r 0

2    |    9 r 0

2    |    4 r 1

2    |    2 r 0

2    |    1 r 0

     |    0 r 1

Reading upwards gives 72 = 1001000₂

(d) Convert the decimal part to binary:

0.125 x 2 = 0.25  = 0 [number in front of decimal]

0.25 x 2 = 0.50 = 0  [number in front of decimal]

0.50 x 2 = 1.00 = 1  [number in front of decimal]

0.00 x 2 = 0.00 = 0  [number in front of decimal]

Reading downwards gives 0.125 = 0010₂

(e) Put the two parts together as follows;

    1001000.0010₂

(f) Convert the result in (e) to its base 2 scientific notation:

Move the decimal to just before the leftmost bit as follows;

1.0010000010

In doing so, we have moved over 6 numbers to the left. Therefore, the exponent is 6. Moving to the left gives a positive exponent while moving to the right gives a negative exponent.

Altogether we have;

1.0010000010 x 2⁶

(g) Determine the sign bit of the number and display in binary: Since the number -72.125 is negative, the sign bit is 1.

(h) Determine the exponent bits.

Since this is a double precision conversion, the exponent bias is 1023.

To get the exponent we add the exponent value from (e) to the exponent bias and get;

6 + 1023 = 1029

(i) Convert the exponent to binary:

2    |    1029

2    |    514 r 1

2    |    257 r 0

2    |    128 r 1

2    |    64 r 0

2    |    32 r 0

2    |    16 r 0

2    |    8 r 0

2    |    4 r 0

2    |    2 r 0

2    |    1 r 0

     |    0 r 1

Reading upwards gives 1029 = 10000000101₂

(j) Determine the mantissa bits:

The mantissa is the rest of the number after the decimal of the base 2 scientific notation found in (f) above.

0010000010 from 1.0010000010 x 2⁶                  [Just remove the leftmost 1 and the decimal point]

(k) Combine the three parts: sign bit (1 bit), exponent bits (11 bits) and mantissa bits (52 bits)

sign bit = 1                [1 bit]

exponent bits = 10000000101    [11 bits]

mantissa bits = 0010000010        [10 out of 52 bits]

Then fill out the remaining part of the mantissa with zeros to make it 52 bits.

mantissa bits = 0010000010000000000000000000000000000000000000000000

Putting all together we have

1 10000000101 0010000010000000000000000000000000000000000000000000 as -72.125 in  a IEEE 754 double precision format.

a) is more precise

b) is more accurate

Explanation:

(a) 7.72, 7.74. 7.73. 7.75, 7.74

For this set the average is: (7.72+7.74+7.73+7.75+7.74)/5=7.736

(b) 7.86, 7.90, 7.78, 7.93, 7.83

For this set the average is: (7.86+7.90+7.78+7.93+7.83)/5=7.86

Accuracy refers to the closeness of a measured set of measures to a known value.In our case that the book value is 7.86g/cm3

We can see that the set (b) is more accurate.

Precision correspond to the closeness of the measurements to each other.

We can see that the set of measures a) is more precise, they are more close one of the each other than the set b)

Step-by-step explanation:

(a)   H0: μ_D=0

      Ha: μ_D ≠ 0

b) Find attached the solution

(c)  By technology,

p - value = 0.4437

Hence, the p-value is 0.4437

If it were 197.6 it would be tenths.
If it were 197.67 it would be hundredths.
If it were 197.672 it would be thousandths.
If it were 197.6722 it would be ten-thousands.

197.6722 is precise to the ten-thousands

Yes you are correct because it really is precise and delicate