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3 years ago

In 79,528, what digit is in the thousands place? 7 9 2 8 submit

Mathematics

1 answer:

Greeley [361]3 years ago

3 0

The digit 9 is in the thousands place

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A masonry contractor is preparing an estimate for building a stone wall and gate. He estimates that the job will take a 40-hour

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Solution: Estimated time for the work is 40 hour work week.

Estimated payment to 3 laborers working 40 hours at cost $14 per hour is:

$3\times 40\times 14=$ $1680

Estimated payment to 6 masons working 40 hours at cost $24 per hour is:

$6\times 40\times 24=$ $5760

Estimated cost of material = $3143

Contractor wishes to make a profit of $500

Therefore, the mathematical expression that will give the estimated cost of the job is:

$Cost = 1680+5760+3143+500$

The estimated total cost is:

Cost =$11083

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There are 5 black marbles, 17 blue marbles, 10 brown marbles, and 12 white marbles. What is the ratio of white marbles to all th

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AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

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2 years ago

Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten

Semenov [28]

Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

$Q(t) = Q(0)e^{-rt}$

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that $Q(12) = 0.5Q(0)$

$Q(t) = Q(0)e^{-rt}$

$0.5Q(0) = Q(0)e^{-12r}$

$e^{-12r} = 0.5$

$\ln{e^{-12r}} = \ln{0.5}$

$-12r = \ln{0.5}$

$12r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{12}$

$r = 0.05776$

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

$Q(t) = Q(0)e^{-rt}$

$50 = 200e^{-0.05776t}$

$e^{-0.05776t} = 0.25$

$\ln{e^{-0.05776t}} = \ln{0.25}$

$-0.05776t = \ln{0.25}$

$0.05776t = -\ln{0.25}$

$t = -\frac{\ln{0.25}}{0.05776}$

$t = 24$

It would take 24 minutes for the element to decay to 50 grams

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3 years ago