A(n) __________ equation is an equation that involves one or more absolute value expressions.

A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri

GuDViN [60]

Answer:

1. $\frac{dy}{dt}=ky$

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

$\frac{dy}{dt}$ =Number of bacteria per unit time

$\frac{dy}{dt}\proportional y$

$\frac{dy}{dt}=ky$

Where k=Proportionality constant

2. $\frac{dy}{y}=kdt$ ,y'(0)=100

Integrating on both sides then, we get

$lny=kt+C$

We have y(0)=200

Substitute the values then , we get

$ln 200=k(0)+C$

$C=ln 200$

Substitute the value of C then we get

$ln y=kt+ln 200$

$ln y-ln200=kt$

$ln\frac{y}{200}=kt$

$\frac{y}{200}=e^{kt}$

$y=200e^{kt}$

Differentiate w.r.t

$y'=200ke^{kt}$

Substitute the given condition then, we get

$100=200ke^{0}=200 \;because \;e^0=1$

$k=\frac{100}{200}=\frac{1}{2}$

$y=200e^{\frac{t}{2}}$

Substitute t=2

Then, we get $y=200e^{\frac{2}{2}}=200e$

$y=200(2.718)=543.6=543.6$

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0

3 years ago

The numerator and the denominator of a fraction are thirteen and fifty, respectively. When a certain number is added to this num

Talja [164]

(13 + x)/(50 - x ) = (2/1)
Cross Multiply
2(50-x) = 1(13 + x)
100 - 2x = 13 + x
add 2x to both sides
100 -2x + 2x = 13 + x + 2x
100 = 13 + 3x
Subtract 13 from both sides
100 - 13 = 13 - 13 + 3x
87 = 3x
divide both sides by 3
29 = x

(13 + 29)/(50-29) = 42/21 = 2 to 1 ratio

7 0

2 years ago

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Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 450 seconds a

Gnoma [55]

Answer:

(D)109

Step-by-step explanation:

Mean = 450 seconds

Standard deviation = 50

First, we determine the probability that the expected response time is between 400 seconds and 500 seconds, P(400<x<500)

Using the Z-Score,

$P(\frac{x-\mu}{\sigma}$

From the Z-Score table

P(-1<x<1) = 0.68269

The probability that the expected response time is between 400 seconds and 500 seconds is 0.68269.

Since there are 160 Emergencies

Number whose expected time is between 400 seconds and 500 seconds

$=160 X 0.68269 \approx 109$

6 0

3 years ago

The table represents quadratic function g. Which statement is true about the function?

weqwewe [10]

Answer:

B. The maximum occurs at the function's x-intercept.

Step-by-step explanation:

Given table:

$\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}$

From inspection of the table, we can see that:

$g(-5) = -1$ and
$g(-3) = -1$

This indicates symmetry.

The line of symmetry is the mid-point between the two x-values.

Therefore, the line of symmetry is x = -4

The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a maximum.

As the y-value of the vertex is 0, the maximum occurs at the function's x-intercept.

3 0

1 year ago

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If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?

frosja888 [35]

In a positively skewed distribution, the extreme scores are larger, thus the mean is larger than the median. Since the mean is 122, the only possible median is 118. Therefore, D.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

8 0

2 years ago

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