What is the solution of the equation -(5/3)x+9=2^(x-1)?

The selling price for a classic speedboat is $12,000. what was the speedboats original price if it is currently selling for $2,0

dangina [55]

Answer:

$7,000

Step-by-step explanation:

Let $x$ equal the original price.

$12,000+2000=2x$

Combine like terms.

$14,000=2x$

Divide by the coefficient of $x$ , which in this case is $2.$

$7,000=x$

If you like the variable on the left, rewrite:

$x=7,000$

4 0

3 years ago

A catering company provides packages for weddings and for showers. The cost per person for small groups

Tomtit [17]

Using the <em>normal distribution and the central limit theorem</em>, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

When two variables are subtracted, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances.

<h3>What is the mean and the standard error of the distribution of differences?</h3>

For each sample, they are given by:

$\mu_W = 82.3, s_W = \frac{18.2}{\sqrt{9}} = 6.0667$

$\mu_S = 65, s_S = \frac{17.73}{\sqrt{6}} = 7.2382$

For the distribution of differences, we have that:

$\mu = \mu_W - \mu_S = 82.3 - 65 = 17.3$

$s = \sqrt{s_W^2 + s_S^2} = \sqrt{6.0667^2 + 7.2382^2} = 9.4444$

The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, <u>one subtracted by the p-value of Z when X = 0</u>, hence:

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

By the Central Limit Theorem

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

$Z = \frac{0 - 17.3}{9.4444}$

$Z = -1.83$

$Z = -1.83$ has a p-value of 0.0335.

1 - 0.0335 = 0.9665.

More can be learned about the <em>normal distribution and the central limit theorem</em> at brainly.com/question/24663213

5 0

2 years ago

Would you use the median or mean to describe the center of each data set? Explain your reasoning. Heights of 50 basketball playe

Ludmilka [50]

Answer:

Median is used to describe the center of the data of heights of 50 basketball players.

Step-by-step explanation:

The median divides the data into two equal parts.

It can be used to describe the center of the data.

The mean gives the average where most data lies.

The advantages of median are

1)it is located even when the values are not capable of quantitative measurements.

2) It is not affected by extreme values > It can be computed even when a frequency distribution involves open end classes like those of income and prices.

3) In a highly skewed distribution median is appropriate average to use.

The disadvantages of the mean are

1) it is greatly affected by extreme values.

2) It sometimes gives fallacious conclusions.

3) In a highly skewed distribution mean is not an appropriate average to use.

4) It cannot be computed even when a frequency distribution involves open end classes like those of income and prices.

4 0

3 years ago

Calcule:

fgiga [73]

E and f were a little complicated.

5 0

3 years ago

The table shows the results of a random survey of kids between the ages of 10 and 15 about their favorite food.

Juliette [100K]

The exact number is 121.966019, so if you round to the nearest whole number, the answer is 122.

5 0

3 years ago