Points A and B lie on line EF.

Item 5 Let f(x)=2 (3) x+1 +4 . The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x) . What is th

insens350 [35]

Answer:

$g(x)=4(3)^{x+1}+8$

Step-by-step explanation:

Given:

The original function is given as:

$f(x)=2(3)^{x+1}+4$

The above function is stretched vertically by a factor of 2 to form the graph of $g(x)$ .

According to the rule of function transformations, when the graph of a function is stretched in the vertical direction by a factor of 'C', where, 'C' is a number greater than 1, then the function rule is given as:

$f(x)\to Cf(x)$

Therefore, the function is multiplied by a factor of 'C' to get the equation of the stretched function.

Here, the the value of 'C' is 2. So, the equation of $g(x)$ is given as:

$g(x)=2f(x)\\g(x)=2[2(3)^{x+1}+4]\\g(x)=4(3)^{x+1}+8$

Therefore, the equation of $g(x)$ is $g(x)=4(3)^{x+1}+8$ .

8 0

3 years ago

The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 oun

vekshin1

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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 Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761$

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

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

By the Central Limit Theorem

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

$Z = \frac{15.99 - 16.15}{0.0761}$

$Z = -2.1$

$Z = -2.1$ has a pvalue of 0.0179

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

3 0

2 years ago

You buy butter for $3.31 a pound.

Sav [38]

Answer:

$0.23

Step-by-step explanation:

Theres 16 ounces in a pound. 16-1.7=14.3

divide $3.31 by 14.3

0.23

8 0

3 years ago

Read 2 more answers

Saul tosses a coin 20 times and determines that the probability of turning heads is 0.55. Determine if this situation is theoret

strojnjashka [21]

Answer: Experimental Probability

Step-by-step explanation:

Theoretical Probability is the theory behind probability. Experimental (empirical) probability is probability calculated during experiments, direct observation, experience, or practice. The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

7 0

2 years ago

Forty minutes of hot yoga and 10 minutes of jumping jacks burns 510 calories. Thirty minutes at hot yoga and 20 minutes of jumpi

son4ous [18]

Answer:

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Step-by-step explanation:

ur answer I have the link

8 0

2 years ago