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2 years ago

4,183 divided by 47 for a quiz

Mathematics

2 answers:

vivado [14]2 years ago

8 0

Answer:

Step-by-step explanation:

docker41 [41]2 years ago

7 0

The answerr to the question is 89

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9. Determine how long it takes for 80% of the material to decay.

Vilka [71]

Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

$A(t) = A(0)e^{-kt}$

In which:

k is the decay rate, as a decimal.

A(0) is the initial amount.

The half-life is of 8 days, hence $A(8) = 0.5A(0)$ , and this is used to find k.

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-8k}$

$e^{-8k} = 0.5$

$\ln{e^{-8k}} = \ln{0.5}$

$-8k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{8}$

$k = 0.08664339757$

Hence:

$A(t) = A(0)e^{-0.08664339757t}$

The time it takes for 80% of the material to decay it t for which $A(t) = 0.2A(0)$ , hence:

$0.2A(0) = A(0)e^{-0.08664339757t}$

$e^{-0.08664339757t} = 0.2$

$\ln{e^{-0.08664339757t}} = \ln{0.2}$

$-0.08664339757t = \ln{0.2}$

$t = -\frac{\ln{0.2}}{0.08664339757}$

$t = 18.6$

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

5 0

2 years ago

Consider the data points (–4, –14), (–2, –7), (0, –3), (2, –2), and (6, –6). Which type of function would best model the data se

Lunna [17]

The solution is attached as a word file

Download doc

3 0

3 years ago

Read 2 more answers

If there are 100 students in a Masters Degree program at OU, and there`s a 5% failure rate, how many students are left after 12

Leviafan [203]

5% fail
so 100-5=95% are left

percent means parts out of 100
95% of 100 is $\frac{95}{100}$ times 100=95

95 students are left assuming that the 5% that fail fail within 12 months

5 0

2 years ago

The staff at Barnett Junior High School went from 40 to 29 employees during the pandemic. What is the percent decrease in staff?

steposvetlana [31]

Answer:

65% - 55%

Step-by-step explanation:

4 0

2 years ago

A cyclist averages 18.5 miles per hour. how many minutes will it take for him to complete a 125 kilometer race?

rjkz [21]

step 1
convert miles to km
1 mile is-----> 1.60934 km
18.5 miles/hour-----> 18.5*1.60934=29.77 km/hour

step 2
convert km/hour to km/minutes
29.77 km/hour--------> 29.77/60----> 0.4962 km/minutes

step 3
by proportion
0.4962 km/1 minutes=125 km/x minutes
0.4962 km----------> 1 minute
125 km-------------> x

x=125/0.4962----> x=251.91 minutes---------> x=251.9 minutes

the answer is
251.9 minutes

Alternative Method

step 1
convert km to miles
1 km is-----> 0.621371 miles
125 km-----> 125*0.621371--->77.67 miles

step 2
convert miles/hour to miles/minutes
18.5 km/hour--------> 18.5/60----> 0.3083 miles/minutes

step 3
by proportion
0.3083 miles/1 minutes=77.67 miles/x minutes
0.3083 miles----------> 1 minute
77.67 miles-------------> x

x=77.67/0.3083----> x=251.9 minutes

6 0

3 years ago