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4 years ago

Why is a number raised to the zero power ALWAYS one and never any other number?

1 answer:

5 0

Do you know how to simplify, let's say for example, x⁵/x² ?

When the bases are the same, you can just subtract the exponent in
the denominator from the exponent in the numerator. So x⁵/x² = x³ .

Now look at x⁷/x⁷ . From that same handy tip, x⁷/x⁷ = x⁰ .

BUT ... any fraction with the same number on top and bottom
is equal to ' 1 '. So x⁰ = 1 , no matter what 'x' happens to be.

Does that do anything for you ?

You might be interested in

A rectangular pool is 7 feet wide. It is 3 times as long as it is wide.

aliina [53]

Answer:

7x21

Step-by-step explanation:

First, we need to find the length of the pool. Since it is three times as long as it is wide, it is 21 feet long (7 x 3 = 21). That way we can tell that it is 7x21, with a perimeter of 56 feet, and an area of 147 feet squared.

4 0

3 years ago

At what point do the lines y = 6x – 18 and<br> y=8x – 32 intersect?

anzhelika [568]

Answer:

(7, 24)

Step-by-step explanation:

Solve the system:

6x - 18 = 8x - 32

2x = 14

x = 7

y = 6(7) - 18

y = 24

4 0

3 years ago

Two lines have the given equations. Use the LINEAR COMBINATION METHOD to solve.

Maurinko [17]

Using linear combination method, the solution to given system of equations are (-7, -15)

<h3><u>Solution:</u></h3>

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated

Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.

<u><em>Given system of equations are:</em></u>

2x - y = 1 ---- eqn 1

3x - y = -6 ------ eqn 2

Subtract eqn 2 from eqn 1

2x - y = 1

3x - y = -6

(-) -------------

-x = 7

Substitute x = -7 in eqn 1

2(-7) - y = 1

-14 - y = 1

y = -14 - 1 = -15

Thus the solution to given system of equations are (-7, -15)

8 0

3 years ago

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m

love history [14]

Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is $c = 20.6153$ .

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be solved using 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.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that $\mu = 20.4, \sigma = 1.23$

Consider the sample mean weight of 100 watermelons of this variety. This means that $n = 100$ .

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123$

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when $X = 20.27$ .

Since we are working with the sample mean, we use $s$ instead of $\sigma$ in the Z score formula

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

$Z = \frac{20.27 - 20.4}{0.123}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of $X = c$ that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use $Z = 1.75$

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

$1.75 = \frac{c - 20.4}{0.123}$

$c - 20.4 = 0.123*1.75$

$c = 20.6153$

This value is $c = 20.6153$ .

6 0

3 years ago

HELP ME OUT! Triangle ABC is transformed by a rotation about the

WARRIOR [948]

Answer : 180 degrees

2 units left

5 units down

Your welcome ❤️

8 0

3 years ago