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konstantin123 [22]

2 years ago

7

The number of bacteria in a petri dish is 50,000 (on day 0) if the amount is doubling each day by when will the number of bacter

ia be 400,000. Let x represent the number of days and f(x) represent the amount of bacteria. Write an equation.

1 answer:

Drupady [299]2 years ago

5 0

Answer:

f(x) = 50000*2^x
3 days

Step-by-step explanation:

<u>Given:</u>

Initial amount of bacteria = 50000
Growth rate = 2 times a day

<u>Required equation:</u>

f(x) = 50000*2^x

<u>Solve for x:</u>

400000 = 50000*2^x
2^x = 400000/50000
2^x = 8
2^x = 2^3
x = 3

After 3 days bacteria numbers will reach 400000

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Elena-2011 [213]

16 because 2•0 is 0. 8-0 is 8 and 2(8) is 16

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3 years ago

Mezclas de alimentos. Un chef repostero creó una solución de azúcar de 50 onzas constituida por 34% de azúcar con una solución d

Kay [80]

Answer:

Las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.

Step-by-step explanation:

Podemos estimar la proporción de ingredientes mediante el siguiente promedio ponderado:

$0.34= \frac{0.2\cdot m_{A} + 0.4\cdot m_{B}}{m_{A}+m_{B}}$ (1)

Donde:

$m_{A}$ - Masa de la solución al 20 %, en onzas.

$m_{B}$ - Masa de la solución al 40 %, en onzas.

Podemos simplificar la formula como sigue:

$0.2\cdot x + 0.4\cdot (1-x) = 0.34$ (2)

Donde $x$ es la proporción de la solución al 20 % dentro de la solución final, sin unidades.

Ahora resolvemos para $x$ en (2):

$0.4-0.2\cdot x = 0.34$

$0.2\cdot x = 0.06$

$x = \frac{0.06}{0.2}$

$x = 0.3$

Este resultado quiere decir que la solución al 34 % es el resultado de 30 % de la solución al 20 % y 70 % de la solución al 40 %. Si conocemos que la solución final tiene una masa de 50 onzas, entonces las cantidades empleadas para su preparación son: 15 onzas de solución al 20 % y 35 onzas de solución al 40 %.

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3 years ago

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2 years ago

solniwko [45]

Answer:

7.2 units

Step-by-step explanation:

Coordinates of city A = (0, 0)

Coordinates of city B = (6, 4)

Use the distance formula to find the distance between the two cities as follows:

$AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(0, 0) = (x_1, y_1)$

$B(6, 4) = (x_2, y_2)$

Plug in the values into the formula

$AB = \sqrt{(6 - 0)^2 + (4 - 0)^2}$

$AB = \sqrt{(6)^2 + (4)^2}$

$AB = \sqrt{36 + 16} = \sqrt{52}$

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6 0

3 years ago

Consider the probability that greater than 94 out of 153 people will not get the flu this winter. Assume the probability that a

Hatshy [7]

Answer:

0.8212 = 82.12% probability that greater than 94 out of 153 people will not get the flu this winter.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.65, n = 153$ . So

$\mu = E(X) = 153*0.65 = 99.45$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.65*0.35} = 5.9$

Consider the probability that greater than 94 out of 153 people will not get the flu this winter

This probability is 1 subtracted by the pvalue of Z when X = 94. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{94 - 99.45}{5.9}$

$Z = -0.92$

$Z = -0.92$ has a pvalue of 0.1788

1 - 0.1788 = 0.8212

0.8212 = 82.12% probability that greater than 94 out of 153 people will not get the flu this winter.

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3 years ago