Which one is the answer for these qution 4x=5(9x+2)<br> A)5/2<br> B)41/10<br> C)-10/41<br> D)10/41

I'm studying a new bacteria that doubles in numbers every 25 minutes. If i start with 50 bacteria, how long until i have 5 milli

dimaraw [331]

Answer:

415.63 minutes

Step-by-step explanation:

Growth can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it grows by using t=25 minutes and $\frac{A_{0}}{A} =2$ or double the amount at that time. The first step we always take is to divide $A_0$ by A.

$[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}$

$2=e^{(25)r}$

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 25.

We solve with a calculator $\frac{ln2}{25} =r\\0.0277=r$

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is $A=A_0e^{0.0277t}$ .

We repeat the step above substituting A=5,000,000, $A_0$ =50, and r=0.02777. Then solve for t.

$5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t$

t=415.63 minutes

6 0

3 years ago

A sphere has a diameter of 14 ft. Which equation finds the volume of the sphere?

aev [14]

Answer:

The volume of the sphere is 1436 in³

The equation is

V = ⁴⁄₃ * 3.14 * (7ft)³

Step-by-step explanation:

radius = half of diameter

d = 14ft

r = 14ft / 2 = 7ft

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius = 7ft

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (7ft)³

V = 4.187 * 343 in³

V = 1436 in³

The volume of the sphere is 1436 in³

6 0

3 years ago

Graph the equation y=147x+60

tiny-mole [99]

If you put the equation into graphing calculator online or manual, you can get the graph.

7 0

3 years ago

Add. 6 1/3 + 4 ¾ + 3 7/12 =

vodka [1.7K]

14 2/3 This is the answer! I know you will get this right buddy!

3 0

2 years ago

Read 2 more answers

8 freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on a committee.

loris [4]

Answer: 11113200

Step-by-step explanation:

We know that , the number of combination of choosing r things from n things is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-

$^8C_4\times ^9C_5\times^9C_2\times^7C_3$

$=\dfrac{8!}{(8-4)!4!}\times\dfrac{9!}{(9-5)!5!}\times\dfrac{9!}{(9-2)!2!}\times\dfrac{7!}{3!(7-3)!}\\\\ =\dfrac{8\times7\times6\times5\times4!}{4!4!}\times\dfrac{9\times8\times7\times6\times5!}{4!5!}\times\dfrac{9\times8\times7!}{7!2!}\times\dfrac{7\times6\times5\times4!}{3!4!}\\\\=11113200$

∴ The number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors = 11113200

6 0

3 years ago

Which one is the answer for these qution 4x=5(9x+2) A)5/2 B)41/10 C)-10/41 D)10/41