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dybincka [34]
3 years ago
14

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of

the plant when it is 19 inches tall? plant height t, time in months h, height in inches 1 18 2 18. 21 3 18. 33 4 18. 42 5 18. 48 6 18. 54 10 months 14 months 16 months 28 months
SAT
1 answer:
Lelechka [254]3 years ago
5 0

The best estimate for the age of the plant at 19 inches tall height is; 28 months

<h3>How to use a logarithmic Model?</h3>

We are given the time in months as;

1, 2, 3, 4, 5, 6 months.

We are also given the corresponding heights for those months respectively as; 18.2, 18.21, 18.33, 18.42, 18.46, 18.54

Now, when we punch those values into an online regression calculator, we arrive at the regression equation as;

y = 18.001 + 0.3ln(x)

We want to find the best estimate for the age of the plant at 19 inches tall height. Plugging in 19 for x in the regression equation gives;

y = 18.001 + 0.3ln(19)

Solving theis gives; y = 28 months

Read more about Regression equation at; brainly.com/question/26755306

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Using the Central Limit Theorem, it is found that the valid conclusion is given as follows:

The sampling distribution will probably not follow a normal distribution, hence we cannot draw a conclusion.

<h3>Central Limit Theorem</h3>

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have a skewed variable with a sample size less than 30, hence the Central Limit Theorem cannot be applied and the correct conclusion is:

The sampling distribution will probably not follow a normal distribution, hence we cannot draw a conclusion.

To learn more about the Central Limit Theorem, you can check brainly.com/question/24663213

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How many grams of sucrose, c12h22o11, must be added to 500. G of water at 100°c to change the vapor pressure to 752 mm hg?.
denpristay [2]

The mass number of sucrose that must be added to 500 g of water is 100.979 grams

To be able to solve this question, we need to use the number of moles concept and mole fraction concept.

<h3>What is the number of moles?</h3>

The number of moles is related to the mass of the substance divided by the molar mass of the substance.

From the given parameters;

The number of moles of water = mass/molar mass

  • Mass of water = 500 g
  • the molar mass of water = 18.02 g/mol

number of moles = 500 g/ 18.02 g/mol

number of moles = 27.75 moles

However,

  • the standard vapor pressure of the solvent \mathbf{P^0_{water}} = 760 mmHg
  • the vapor pressure of the solute = 752 mmHg

Using the mole concept:

\mathbf {X_{C_{12}H_{22}O_{11}} = \dfrac{n_{C_{12}H_{22}O_{11}}}{n_{H_2O}+n_{C_{12}H_{22}O_{11}}} }

By relative lowering of vapor pressure:

\mathbf{\dfrac{P^0_{H_2O} - P_{H_2O}}{P^0_{H_2O}} = X_{C_{12}H_{22}O_{11}}}

\mathbf{\dfrac{760 -752}{760} = \dfrac{n_{C_{12}H_{22}O_{11}}}{27.75 +n_{C_{12}H_{22}O_{11}}} }}

\mathbf{0.01053 = \dfrac{n_{C_{12}H_{22}O_{11}}}{27.75 +n_{C_{12}H_{22}O_{11}}} }}

\\ \\ \mathbf{0.01053 (27.75) +0.01053 (n_{C_{12}H_{22}O_{11}} ) = n_{C_{12}H_{22}O_{11}}}

\\ \\ \mathbf{0.2922075 =0.98947&#10; (n_{C_{12}H_{22}O_{11}} )}

\\ \\ \mathbf{ (n_{C_{12}H_{22}O_{11}} ) = \dfrac{0.2922075 }{0.98947}}

\\ \\ \mathbf{ (n_{C_{12}H_{22}O_{11}} ) =0.295 \ moles}

The mass of sucrose = number of moles × molar mass

The mass of sucrose = 0.295 moles × 342.3 g/mol

The mass of sucrose = 100.979 grams

Learn more about number of moles here:

brainly.com/question/13314627

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