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gregori [183]
4 years ago
10

Ship Co. produces storage crates that require 1.2 meters of material at $.85 per meter and 01 direct labor hours at $15.00 per h

our Overhead is applied at the rate of $9 per direct labor hour What is the total standard cost for one unit of product that would appear on a standard cost card?
Mathematics
1 answer:
Vesna [10]4 years ago
5 0

Answer:

$3.42

Step-by-step explanation:

Meters of material required = 1.2 meters

Cost per meter of material = $0.85

Direct labor hours = 0.1

Cost of direct labor per hour = $15

Overhead rate = $9 per direct labor hour

Standard cost per unit of product :

(Direct material cost per unit + direct labor cost per unit + overhead cost per unit)

Direct material cost per unit :

Material needed × cost per meter = (1.2 × $0.85) = $1.02

Direct labor cost per unit :

Direct labor hour × cost per hour = ( 0.1 × $15) = $1.5

Overhead cost:

0.1 * $9 = $0.9

Standard cost :

($1.02 + $1.5 + $0.9) = $3.42

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
Viktor [21]

When n=0, we have

5^{3^0} + 1 = 5^1 + 1 = 6

3^{0 + 1} = 3^1 = 3

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for n=k, that

3^{k + 1} \mid 5^{3^k} + 1

Now for n=k+1, we have

5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)

so we know the left side is at least divisible by 3^{k+1} by our assumption.

It remains to show that

3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1

which is easily done with Fermat's little theorem. It says

a^p \equiv a \pmod p

where p is prime and a is any integer. Then for any positive integer x,

5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3

Furthermore,

5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3

which goes all the way down to

5^{3^k} \equiv 5 \pmod 3

So, we find that

\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3

QED

5 0
2 years ago
Susanne checks the temperature at 11:00 a.m. She notices that, if the
Ivahew [28]

Answer:

if you want to know the temperature it's 78

Step-by-step explanation:

84-6 is 78

4 0
3 years ago
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strojnjashka [21]

Answer:

 

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Step-by-step explanation:

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3 years ago
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Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Ar
Yanka [14]

Answer:

11.29.

Step-by-step explanation:

We are given that The mean length of six-year-old rainbow trout in the Arolik River in Alaska is 478 millimeters with a standard deviation of 38 millimeters.

We are also given that these lengths are normally distributed.

So, The highest value is at mean .(Refer the attached figure).

Formula : Percentile = \frac{Length}{Maximum} \times 100

54 = \frac{Length}{478} \times 100

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4 0
4 years ago
50% of what number is 31
Ivenika [448]

To find 50% or half, of 31, you can just add 31 + 31.

Or, 31 x 2.

Or even the longer way, we know 3 + 3 = 6. So we can just add 0's: 30 + 30 = 60. That leaves us with the 1's. 1 + 1 = 2.

Take our 60 from earlier, and add 2. 60 + 2 = 62.

Check your answer. 62/2 = 31.

Your answer is 62

6 0
3 years ago
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