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yanalaym [24]
4 years ago
7

The time to assemble the first unit on a production line is 8 hours. The learning rate is 0.81. Approximately how long will it t

ake for the seventh unit to be​ assembled?
Mathematics
1 answer:
pochemuha4 years ago
3 0

Answer:

4.428 hours

Step-by-step explanation:

If the learning rate is 0.81, the slope of the learning curve is:

b=\frac{ln(0.81)}{ln(2)} \\b=-0.304

The time it takes to produce the n-th unit is:

T_n=T_1*n^b

If T1 = 8 hours, the time required to produce the seventh unit will be:

T_n=8*7^{-0.304}\\T_n=4.428\ hours

It will take roughly 4.428 hours.

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lutik1710 [3]

Answer:

The population of California is 3.3216 * 10^{7} more than the population of Wyoming.

Alternatively, the population of California is 6.64 * 10^{1} times the population of Wyoming.

Step-by-step explanation:

The first part is to take the numbers out of the scientific notation. The estimated population of California is 38,800,000, and the population of Wyoming is 584,000.

Not that we've done that, let's start with the first part of the problem.

"The population of California is __________ more than the population of Wyoming."

This is a statement of subtraction, because it's not asking how many TIMES more. So, we subtract Wyoming's population from California's population.

38,800,000 - 584,000 = 38,216,000.

Putting that number into scientific notation is easy: move the decimal to the place in the number where there will only be one number in front of the decimal: 3.3216. How many number slots until you have only one number in front of the decimal? 7. So, we know that the power of 10 is going to be 7. So, the first part of the question answers to:

3.8216 * 10^{7} .

Now for the second part.

"Alternatively, the population of California is _________ times the population of Wyoming."

This is a problem of division. The question is asking us to divide California's population by Wyoming's population.

\frac{38,800,000}{584,000} = 0.664383562 * 10^{2} .

We need to have one number in front of the decimal point, so we move it behind the first 6, giving us 6.64. Because we did this, we need to bump the exponent from 2 to 1, leaving us with:

6.64 * 10^{1}.

So, the answer to the question is:

1. 3.8216 * 10^{7}.

2. 6.64 * 10^{1}.

Hope this helped you, and I hope you get a perfect score!! :)

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3 years ago
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3 years ago
The product of two consecutive positive integers is 1111 more than their sum. find the integers.
Alex787 [66]
The correct question is
<span>The product of two consecutive positive integers is 11 more than their sum. find the integers.

Let
x-------> the first </span>positive integer
x+1-----> the second consecutive positive integer

we know that
x*(x+1)=11+(x+(x+1))----> x²+x=11+(2x+1)----> x²+x=2x+12
x²-x-12=0

using a graph tool------> to resolve the second order equation
see the attached figure

the solution is
x=4

therefore

the numbers are
x=4
x+1=5

the answer is
the numbers are 4 and 5

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3 years ago
An inclined ramp rises 5ft over a horizontal distance of 10ft. How long is the ramp?
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3 years ago
A construction company can remove 3/3/4 metric tons of dirt from a construction site in 1/1/8 hours what is the unit rate in met
kotykmax [81]

Answer:

3 1/3 metric tons per hour

Step-by-step explanation:

To find the unit rate, divide 3 3/4 metric tons by 1 1/8 hours (notice that the correct format is 3 3/4, not 3/3/4).

 3 3/4 metric tons       3.75 metric tons

---------------------------- = --------------------------

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It's easier to deal with decimal fractions here than with proper fractions.

The unit rate then comes out to be 3.75/1.125 metric tons per hour, or

3.33333 metric tons per hour, or   3 1/3 metric tons per hour

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3 years ago
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