Which ordered pair is a solution to the system of inequalities? y <3 and y >-x+5 ?

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

7 0

It should be A 6,1 because 6 is the x-axis and 1 is the y-axis

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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

4 years ago

The two-way table shows the number of people whose hobbies are reading or solving puzzles and who either ride a motorcycle or do

enot [183]

The number of people whose hobby is reading but not riding a motorcycle is 5.

<h3>What is the relative frequency of not riding a motorcycle?</h3>

We want to calculate the number of people whose hobby is reading but they don't like riding the motorcycle,

therefore, when we look into the table we will find out that block A2 is the block that represents the number of people whose hobby is reading but not riding a motorcycle.

Hence, the number of people whose hobby is reading but not riding a motorcycle is 5.

Learn more about Relative frequency:

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