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2 years ago

Find the missing value for the exponential function represented by the table below x -2 -1 0 1 2 y 29 20.3 14.21 6.9629

Mathematics

1 answer:

andre [41]2 years ago

5 0

Answer:

y=4.8710 is the missing value

Step-by-step explanation:

The first step in approaching this question is determining the exponential equation that models the set of data. This can easily be done in Ms.Excel application. We first enter the data into any two adjacent columns of an excel workbook. The next step is to highlight the data, click on the insert tab and select the x,y scatter-plot feature. This creates a scatter-plot for the data.

The next step is to click the Add chart element feature and insert an exponential trend line to the scatter plot ensuring the display equation on chart is checked.

The exponential regression equation for the data set is given as;

$y=12.321e^{-0.464x}$

To find the missing y value, we simply substitute x with 2 in the regression equation obtained;

$y=12.321e^{-0.464(2)}\\\\y=4.8710$

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In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in t

victus00 [196]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that he or she would choose the pair of socks in the center position is $p =\frac{1}{5}$

The correct answer choice is

X has a binomial distribution with parameters n=100 and p=1/5

The mean is $\mu = 20$

The standard deviation is $\sigma=4$

The probability, $P =0.0002$

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

Using the R the probability $Pe = 0.0003$

The probabilities $P \approx Pe$

Step-by-step explanation:

Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as

$p =\frac{1}{5}$

$=0.2$

The mean of this distribution is mathematical represented as

$\mu = np$

substituting the value

$\mu = 100 * 0.2$

$\mu = 20$

The standard deviation is mathematically represented as

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

substituting the value

$= \sqrt{100 * 0,2 (1-0.2)}$

$\sigma=4$

Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as

$P=P(X \ge 34 )$

By standardizing the normal approximation we have that

$P(X \ge 34) \approx P(Z \ge z)$

Now z is mathematically evaluated as

$z = \frac{x-\mu}{\sigma }$

Substituting values

$z = \frac{34-20}{4}$

$=3.5$

So using the z table the $P(Z \ge 3.5)$ is 0.0002

The probability P and Pe that 34 or more subject would choose the center pair is very small So

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.