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3 years ago

Please help fast HELP

Mathematics

1 answer:

Sveta_85 [38]3 years ago

5 0

Answer:

The letters are really small I can't see it.

Step-by-step explanation:

Sorry

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Write 3 different ways to correctly compare the following numbers. use ≥, ≤, or ≠ 352 352

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Three ways to correctly compare the following numbers are, 352 = 352, anything else is impossible with < and >

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Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university, however, she must pay

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It would be about 2938 Euros.

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3 years ago

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Suppose that a Petri dish initially contains 2000 bacteria cells. An antibiotic is introduced and after 4 hour, there are now 16

Sergeu [11.5K]

Answer:

a)The linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b)The exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

Step-by-step explanation:

(a) Suppose that P(t) is a linear function. Find a formula for P(t):

$P(t)$ can be modeled by a linear function in the following format.

$P(t) = P_{0} - r*t$ , in which $P_{0}$ is the initial number of bacteria cells in the dish, t is the time and r is the rate that the number decreases.

Since the dish initially contains 2000 bacteria cells, $P_{0} = 2000$

We have

$P(t) = 2000 - r*t$

An antibiotic is introduced and after 4 hour, there are now 1600 bacteria cells present. So $P(4) = 1600$ . With this information, we can find the value of r.

$P(t) = 2000 - r*t$

$1600 = 2000 - r*(4)$

$4r = 400$

$r = \frac{400}{4}$

$r = 100$

So, the linear function for $P(t)$ is:

$P(t) = 2000 - 100*t$

b) Suppose that P(t) is an exponential function. Find a formula for P(t)

$P(t)$ can also be modeled by an exponential function in the following format:

$P(t) = P_{0}e^{rt}$

The values mean the same as in a). We use the fact that $P(4) = 1600$ to find r.

$P(t) = 2000e^{rt}$

$1600 = 2000e^{4r}$

$e^{4r} = \frac{1600}{2000}$

$e^{4r} = 0.8$

$ln e^{4r} = ln 0.8$

$4r = -0.22$

$r = \frac{-0.22}{4}$

$r = -0.055$

So, the exponential function for $P(t)$ is:

$P(t) = 2000e^{-0.055t}$

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4 years ago

Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532

IgorC [24]

The answer is chicken $8, duck $5

x - the cost of a chicken
y - the cost of a duck

he sold 50 chickens and 30 ducks for $550: 50x + 30y = 550
he sold 44 chickens and 36 ducks for $532: 44x + 36y = 532

50x + 30y = 550 divide by 10
44x + 36y = 550 divide by 4
______________
50x/10 + 30y/10 = 550/10
44x/4 + 36y/4 = 532/4
______________
5x + 3y = 55 Multiply by (-3)
11x + 9y = 133
______________
5x * (-3) + 3y * (-3) = 55 * (-3)
11x + 9y = 133
______________
-15x - 9y = -165
11x + 9y = 133
______________
Sum up:
-4x + 0y = -32
-4x = -32
x = -32/-4
x = 8

Since 5x + 3y = 55 and x = 8, then:
5 * 8 + 3y = 55
40 + 3y = 55
3y = 55 - 40
3y = 15
y = 15/3
y = 5

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3 years ago

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