- 4x + 8y = 20<br> ----4x + 2y = -30

Help I will mark brain list.

artcher [175]

Answer: the area equals 580

Step-by-step explanation: the area is length times height times width and it all equals to 580

hope this helps

4 0

2 years ago

Convert the rainfall amounts to feet and make a new line plot.

Cerrena [4.2K]

Answer:

46in

Step-by-step explanation:

brainiest is appreciated

3 0

2 years ago

Read 2 more answers

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

3 years ago

Joseph claims that a scatterplot in which the y-values increase as the x-values increase must have a linear association. Amy cla

My name is Ann [436]

Answer: Choice C

Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.

======================================================

Explanation:

Just because the data points trend upward (as you go from left to right), it does not mean the data is linearly associated.

Consider a parabola that goes uphill, or an exponential curve that does the same. Both are nonlinear. If we have points close to or on these nonlinear curves, then we consider the scatterplot to have nonlinear association.

Also, you could have points randomly scattered about that don't fit either of those two functions, or any elementary math function your teacher has discussed so far, and yet the points could trend upward. If the points are not close to the same straight line, then we don't have linear association.

-----------------

In short, if the points all fall on the same line or close to it, then we have linear association. Otherwise, we have nonlinear association of some kind.

Joseph's claim that an increasing trend is not enough evidence to conclude the scatterplot is linear or not.

8 0

3 years ago

*will give brainist*<br><br> just make sure the answer is correct!!

slavikrds [6]

I think 86

you’d just add 26 and 60

4 0

2 years ago

- 4x + 8y = 20 ----4x + 2y = -30