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3 years ago

Calculate the quotient and remainder of –1 divided by 3.

Mathematics

1 answer:

gtnhenbr [62]3 years ago

3 0

I don't understand how a fraction can have a remainder cause normally the remainder is a fraction.

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A cell of some bacteria divides into two cells every 10 minutes.The initial population is 3 bacteria. (a) Find the size of the p

mars1129 [50]

Answer:

(a) $P_{t}=3(2)^{6t}$

(b) $3(2)^{42}$

Step-by-step explanation:

A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.

That means sequence formed will be 3, 6, 12, 24............

We can easily say that this sequence is a geometric sequence having common ratio (r) = $\frac{T_{2}}{T_{1}}=\frac{6}{3}$

r = 2

Now we know the explicit formula of a geometric sequence is given by

$P_{t}=P_{0}(r)^{\frac{60t}{10}}=P_{0}(r)^{6t}$

Where a = Initial population = 3 bacteria

r = common ratio = 2

and t = time in hours

So explicit formula will be $P_{t}=3(2)^{6t}$

(a) Now we have to calculate the size of population after t hours

$P_{t}=3(2)^{6t}$

(b) We have to find the size of population after 7 hours or 420 minutes

$P_{t}=3(2)^{6\times7}$

= $3(2)^{42}$

After 7 hours bacteria population will be $3(2)^{42}$

By the explicit formula

$21=3(2)^{6t}$

$2^{6t}=\frac{21}{3}=7$

Now we take log on both the sides of the equation

$log(2^{6t})=log(7)$

6t log2 = log 7

6t(0.301) = 0.845

t(1.806) = 0.845

t = $\frac{0.845}{1.806}=0.468$ hours

Or t = 0.468×60 = 28.07 minutes

Therefore, after 28.07 minutes bacterial population will be 21

5 0

3 years ago

gavmur [86]

Given that 2 similar signs have a scale factor of 5:3 and the larger sign is 45 ft, then the smaller sign will have the height given by:
scale factor=(height of large sign )/(height of smaller sign)
let the height of smaller sign be x, plugging in the values we get:
5/3=45/x
solving for x we get
3/5=x/45
hence
x=3/5×45
x=27 ft
The height of smaller sign will be 27 ft

7 0

3 years ago

Which is not a form of ionizing radiation?

IceJOKER [234]

Answer:

Step-by-step explanation:

6 0

3 years ago

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What is the value of the expression if m = -5 and n =<br> มีเล<br> ส « |<br> |

Sliva [168]

Answer:

The answer is 4/25

Step-by-step explanation:

this is the solution

(2(-5)^-1(3)^5/3(3)^4)^2

(2/-5*243/243)^2

(2/-5)^2

4/25

3 0

4 years ago

Ms. Sampson recorded the percentage change in her students

kvv77 [185]

Answer:

The student whose marks between quarter grades & topic tests score has maximum proportionate deviation

Step-by-step explanation:

Percentage change shows the proportionate change in a value, from the initial point. Formula = ( Change / Old ) x 100

Percentage change in students' quarter grades from topic tests score =

[ ( Quarter topic test score - Topic test score ) / Topic Test score ] x 100

Eg : Quarter Grade = 80, Test score = 60.

Percentage change = [ (80 - 60)/ 60 ] x 100 = ( 20 / 60 ) x 100 = 33%

So, student who has this maximum proportionate or percentage deviation between quarter grades & topic tests score - that student change would be represented by the point farthest from 0 on a number line.

5 0

3 years ago

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