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3 years ago

Find the value of X:

Mathematics

1 answer:

sasho [114]3 years ago

7 0

Answer:

x = 5

Step-by-step explanation:

2x+5 = 15

2x = 10

x = 5

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A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich

Bess [88]

Answer:

a). k = 2.0794

b). $A_{t}=A_{0}(2^{3t} )$

c). 13107200 cells

d). rate of growth after 6 hours = 27255112

e). 4.76 hours

Step-by-step explanation:

From the formula of bacterial population,

$A_{t}=A_{0}e^{kt}$

Where $A_{t}$ = Bacterial population after time t

$A_{0}$ = Initial population

k = relative growth factor

t = duration or time

a). For $A_{t}=2\times 50=100$ cells

and $A_{0}=50$ cells

Time t = 20 minutes = $\frac{1}{3}$ hours

Now we plug in these values in the formula,

100 = $50(e^{\frac{k}{3}})$

$e^{\frac{k}{3}}=2$

By taking natural log on both the sides of the equation,

$\frac{k}{3}(lne)=ln(2)$

k = 3ln(2) = 2.0794

b). To get the expression we will plug in the value of k in the formula.

$A_{t}=A_{0}e^{kt}$

Since k = 3ln(2)

$A_{t}=A_{0}e^{3t(ln2)}$

Let y = $e^{3t(ln2)}$

By taking natural log on both the sides of the equation,

lny = $ln(e^{3t(ln2)} )$

lny = 3t(ln2)ln(e)

ln(y) = 3t(ln2)

ln(y) = $ln(2)^{3t}$

y = $2^{3t}$

Now our expression will be $A_{t}=A_{0}(2^{3t} )$

c). Number of cells after t = 6 hours

$A_{6}=50(2^{3\times 6} )$

$A_{6}=50(2^{18})$

$A_{6}=50\times (262144)=13107200$

d). We can get the rate of growth by finding derivative of the expression

$\frac{d}{dt}(A_{t})=\frac{d}{dt}[A_{0}(e^{kt}})]$

= $A_{0}[ke^{kt}]$

Now $\frac{d}{dt}(A_{6})=k.A_{6}$

= 2.0794×13107200

= 27255112

e) From the given formula,

$A_{t}=A_{0}(2^{3t} )$

$1000000=50(2^{3t} )$

$2^{3t}=20000$

3t(ln2) = ln(20000)

t = $\frac{ln(20000)}{3(ln2)}$

t = $\frac{9.90349}{2.07944}=4.76$ hours

3 0

3 years ago

Plz help 7th grade math ASAP

nikklg [1K]

They lost -17 bc they lost -3 yards the first game and then -14 the second

5 0

4 years ago

Helppppp pleaseeee !!!!!!!!!!

rusak2 [61]

Step-by-step explanation:

the 60 preliminary published articles are a constant.

all the new articles are simply added to that to get the total number of published articles.

every months produces 12 more articles.

so,

m = 1 means a = 60 + 1×12 = 72

m = 3 means a = 60 + 3×12 = 60 + 36 = 96

m = 4 means a = 60 + 4×12 = 60 + 48 = 108

m = 9 means a = 60 + 9×12 = 60 + 108 = 168

3 0

3 years ago

A linear function has a slope of 2 and passes through the point (0,6). What is the equation of the line?

pychu [463]

A linear function means you’re working with a line. Lines can be stated in slope-intercept form: y=mx+b.

To make it a linear function, you simply replace “y” with “f(x)” notation: f(x) = mx + b

The information you gave told you m=2 and b=6, since (0,b) is the y-intercept.

Putting that all together you have:
f(x) = 2x + 6

4 0

3 years ago

Which expression has the greatest value?<br> A. 149.2<br> B. 149 - 16<br> C. 25 +16<br> D. 125.3

umka21 [38]

The answer would be A. If I subtracted 149 from 16, I would end up with 133, so it would not be B. If I added 25 to 16, that would equal 41, so that’s not the answer. Lastly, I wouldn’t choose D because 149.2 is greater than 125.3
Remember, any number before a decimal is considered a whole number.

7 0

3 years ago