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2 years ago

Marly drove 15 miles to work and then x miles to the store. How many miles did she travel in total?

Mathematics

2 answers:

enyata [817]2 years ago

7 0

15+x=?
Needs more info

igomit [66]2 years ago

6 0

15+x miles. You can’t give a more specific answer because they don’t give you any other values to work with.

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Determine the 5th term in geometric sequence whose first term is 4 and whose common ratio is 3

amid [387]

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2 years ago

Danny has a rectangular rose garden that measures 8m by 12.5m. One bag of fertilizer can cover 16m2 . How many bags will he need

mrs_skeptik [129]

Answer:

we will need 7 bags

Step-by-step explanation:

To solve this problem we first have to calculate the total area of the garden

a = area

b = base = 8m

h = height = 12.5m

a = b * h

we replace with the known values

a = 8m * 12.5m

a = 100m²

Now that we know the total area of the garden and the area occupied by a single bag, we divide the total area by what a bag covers.

100m² / 16m² = 6.25 bags

because we cannot buy a fraction of a bag we will need 7 bags

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3 years ago

A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal place

Andrej [43]

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

$P(t) = P(0)(1-r)^{t}$

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

$P(1) = 0.97P(0)$

Then

$P(t) = P(0)(1-r)^{t}$

$0.97P(0) = P(0)(1-r)^{0}$

$1 - r = 0.97$

$P(t) = P(0)(0.97t)^{t}$

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.5P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.5$

$\log{(0.97)^{t}} = \log{0.5}$

$t\log{0.97} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.97}}$

$t = 22.76$

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.85P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.85$

$\log{(0.97)^{t}} = \log{0.85}$

$t\log{0.97} = \log{0.85}$

$t = \frac{\log{0.85}}{\log{0.97}}$

$t = 5.34$

5.34 years for the sample to decay to 85% of its original amount

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3 years ago