If the new athletic fee is $22 and the old fee is $20, how much is the percent increase in fees?

What is the justification for the first step in proving the formula for factoring the sum of cubes?

Anna11 [10]

Explanation:

The formula isnt correctly written, it should state:

$a^3+b^3 = (a+b)(a^2-ab+b^2)$

You have to start from $(a+b)(a^2-ab+b^2)$ and end in a³+b³. On your first step, you need to use the distributive property.

$(a+b)(a^2-ab+b^2) = a*(a^2-ab+b^2) + b*(a^2-ab+b^2)$

This is equal to

$a*a^2-a*(ab) + a*b^2 + b*a^2-b*(ab) + b*b^2 = a^3 - a^2b + ab^2 +ba^2 -b^2a +b^3$

Note that the second term, -a²b, is cancelled by the fourth term, ba², and the third term, ab², is cancelled by the fifht term, -b²a. Therefore, the final result is a³+b³, as we wanted to.

5 0

2 years ago

Question 3<br> 1 pts<br> 2 and -2 are 4 units apart on the number line.<br> True<br> False

EastWind [94]

It’s actually true!

^ ^ ^ ^
<—|——|——|——|——|—>
-2 -1 0 1 2

The 4 arrows above the number line represents the distance between 2 and -2 which is 4!

4 0

2 years ago

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

mihalych1998 [28]

Answer: The first option

Step-by-step explanation:

I'm smart

5 0

2 years ago

11/12 as a percentage

evablogger [386]

Answer:

91.67%

Step-by-step explanation:

8 0

1 year ago

Read 2 more answers

The mean salary offered to students who are graduating from Coastal State University this year is , with a standard deviation of

Monica [59]

Answer:

The probability that the mean salary offer is of X or less is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean salary for the population, $\sigma$ is the standard deviation for the population and n is the size of the sample.

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

Z-score with the Central Limit Theorem:

Z-is given by:

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

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

What is the probability that the mean salary offer for these students is X or less?

The probability that the mean salary offer is of X or less is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is the mean salary for the population, $\sigma$ is the standard deviation for the population and n is the size of the sample.

4 0

2 years ago