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Paul [167]
3 years ago
9

A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 13 minutes th

ere are 320 bacteria, after how many minutes will there be 15 bacteria remaining? Round your answer to the nearest whole number.
Mathematics
1 answer:
nikklg [1K]3 years ago
3 0

Answer:

56.42 minutes

Step-by-step explanation:

The initial sample= y0 = 800

After 13 minutes , amount = 320

Y= y0e-kt

320 = 800e-k(13)

320/800 = e-k13

0.4 = e-k13

In0.4 = -k13

-0.91629= -k13

0.07048= k

Y = 800e-0.07048t

Minutes when the bacterial present will be 15

15 = 800e-0.07048t

15/800= e-0.07048t

0.01875 = e-0.07048t

In 0.01875 = -0.07048t

-3.97656 = -0.07048t

-3.97656/-0.07048= t

56.42 = t

56.42 minutes

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Answer:

Jordan had 40 stickers.

Step-by-step explanation:

For this ratio, we have David:Ben:Jordan as 8:9:10, and so we need to make it as a more complex fraction, 8/9/10, now we need a multiplier to get us from 9 stickers of Jordan to 36, like a giant one. The common multiplier in this case is 4, and we know that the values must always stay proportional. We multiply everything by 4,and we get a final ratio of 32:36:40, and since Jordan is the last in the ratio David:Ben:Jordan, Jordan ends up with 40 stickers.

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3 years ago
In parallelogram ABCD, AD = 12 in, m∠C = 46º, m∠DBA = 72º. Find the area of ABCD
dmitriy555 [2]

Answer:

The area of   parallelogram ABCD  is78.42 \mathrm{in}^{2}

Explanation:

Given:

AD = 12 in

m \angle C=46^{\circ}

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To Find:

The area of   parallelogram ABCD=?  

Solution:

When we construct the parallelogram with the given data, we get a parallelogram formed by 12 cm as one side and an angle with 46 degrees.  

The area of the parallelogram can be calculated by a b * \sin (a n g l e)

Substituting the value of a=12  we have

\text { Area of parallelogram }=12 * \text { bsin } 46

<u>To find  the value of b, </u>

We know that area of a triangle can be expressed as,

\text { Area of triangle }=(A b / 2) \sin (\text {angle})

So,

(12 * B D / 2) * \sin 46=(A B * B D / 2) * \sin 72

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12 * \sin 46=A B * \sin 72

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